CLASS 11 PHYSICS • UNITS AND MEASUREMENTS

Measurement and Significant Figures

Master measurement, least count, precision, accuracy, significant figures, rounding, scientific notation and exam-style numerical reporting.

CBSENEETJEE MainJEE AdvancedIBIGCSE PhysicsA-Level

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1. Measurement

Measurement is the process of comparing an unknown physical quantity with a standard unit. A measurement is complete only when it has a numerical value and a unit.

Need of Measurement

Physics laws become testable only through measurements. Experiments require length, time, mass, temperature, current and many other measurements.

Direct Measurement

Measured directly using an instrument, such as length by ruler or mass by balance.

Indirect Measurement

Calculated from other measured quantities, such as density = mass / volume.

QuantityInstrumentValue+ Unit

2. Least Count

Least count is the smallest value that can be measured by an instrument.

Least Count = Value of one smallest division

Ruler

Common ruler has least count 1 mm or 0.1 cm.

Vernier Calipers

Used for diameter, thickness and depth measurements with smaller least count than ruler.

Screw Gauge

Used for very small thickness or diameter, such as wire diameter.

Ruler: smallest division gives least count

3. Precision

Precision means closeness of repeated readings to one another. It indicates repeatability and reproducibility.

Repeatability

Same observer, same instrument and same conditions give close readings.

Reproducibility

Different observers or instruments obtain similar readings.

Example

Readings 2.51 cm, 2.52 cm and 2.51 cm are precise because they are close together.

4. Accuracy

Accuracy means closeness of measured value to the true value. Accuracy and precision are different ideas.

Accurate and preciseAccurate, not precisePrecise, not accurateNeither accurate nor precise

5. Significant Figures

Significant figures are meaningful digits in a measured number. They show the precision of measurement and prevent over-reporting.

Rule TypeExampleStatus
Leading zeros0.00450Not significant
Captive zeros1002Significant
Trailing zeros after decimal2.300Significant
Trailing zeros without decimal1000Ambiguous
Exact numbers12 studentsInfinite significant figures

6. Rules of Significant Figures

0.00450

Leading zeros are not significant. 4, 5 and final 0 are significant. Total = 3.

2.300

All digits including trailing zeros after decimal are significant. Total = 4.

1000

Without decimal, trailing zeros may be ambiguous. Scientific notation removes ambiguity.

1000.

Decimal point shows trailing zeros are significant. Total = 4.

3.00 × 108

Coefficient 3.00 has 3 significant figures.

7. Rounding Off

Rounding off gives an answer with required number of significant figures or decimal places.

SituationExampleResult
Next digit less than 52.342 to 3 SF2.34
Next digit greater than 52.346 to 3 SF2.35
Next digit exactly 5Use standard rounding rule specified by teacher/examUsually round up in school use
Scientific reporting3.456 × 105 to 3 SF3.46 × 105

8. Addition and Subtraction Rules

In addition and subtraction, final answer is written up to the least number of decimal places among given quantities.

ExpressionRaw ResultReported Result
12.11 + 18.0 + 1.01331.12331.1 because least decimal places = 1
5.67 - 2.13.573.6 because least decimal places = 1
0.345 + 2.32.6452.6 because least decimal places = 1

9. Multiplication and Division Rules

In multiplication and division, final answer has the same number of significant figures as the least precise given number.

ExpressionRaw ResultReported Result
2.5 × 3.428.558.6 because 2.5 has 2 SF
12.0 / 3.04.02 SF
1.23 × 4.55.5355.5 because 4.5 has 2 SF

10. Scientific Notation

Scientific notation writes a number as a × 10n, where 1 ≤ a < 10.

NumberScientific Notation
3000000003.00 × 108
0.00000626.2 × 10-6
450004.5 × 104
0.07507.50 × 10-2

11. Important Tables

Significant Figure Rules

Digit TypeRule
All non-zero digitsSignificant
Leading zerosNot significant
Captive zerosSignificant
Trailing decimal zerosSignificant

Operation Rules

OperationReporting Rule
Addition/SubtractionLeast decimal places
Multiplication/DivisionLeast significant figures
RoundingBased on next digit

12. NEET Question Bank: 60 MCQs

NEET MCQ 1

Question: Least count of a metre scale usually is

(a) 1 mm(b) 1 cm(c) 1 m(d) 10 cm

Correct Answer: 1 mm

Explanation: Smallest division on common metre scale is 1 mm.

Exam Tip: Know common least counts.

NEET MCQ 2

Question: Accuracy means closeness to

(a) true value(b) repeated values(c) zero(d) large value

Correct Answer: true value

Explanation: Accuracy compares measured value with true value.

Exam Tip: Accuracy = true value closeness.

NEET MCQ 3

Question: Precision means

(a) repeatability(b) true value closeness(c) large error(d) wrong unit

Correct Answer: repeatability

Explanation: Precision is closeness of repeated readings.

Exam Tip: Precision = reproducibility.

NEET MCQ 4

Question: Number of significant figures in 0.00450 is

(a) 3(b) 2(c) 5(d) 1

Correct Answer: 3

Explanation: Leading zeros are not significant; 4, 5 and final 0 count.

Exam Tip: Leading zeros do not count.

NEET MCQ 5

Question: Number of significant figures in 2.300 is

(a) 4(b) 2(c) 3(d) 1

Correct Answer: 4

Explanation: Trailing zeros after decimal are significant.

Exam Tip: Zeros after decimal count.

NEET MCQ 6

Question: Scientific notation of 0.00072 is

(a) 7.2 × 10-4(b) 72 × 10-5(c) 0.72 × 10-3(d) 7.2 × 104

Correct Answer: 7.2 × 10-4

Explanation: Move decimal four places to right.

Exam Tip: Coefficient must be 1 to 10.

NEET MCQ 7

Question: In addition, final answer follows

(a) least decimal places(b) most significant figures(c) least power(d) largest unit

Correct Answer: least decimal places

Explanation: Addition/subtraction depends on decimal places.

Exam Tip: Decimal place rule.

NEET MCQ 8

Question: In multiplication, final answer follows

(a) least significant figures(b) least decimal places(c) highest value(d) SI prefix

Correct Answer: least significant figures

Explanation: Multiplication/division depends on significant figures.

Exam Tip: Significant figure rule.

NEET MCQ 9

Question: Exact numbers have

(a) infinite significant figures(b) zero significant figures(c) one significant figure(d) two significant figures

Correct Answer: infinite significant figures

Explanation: Counting numbers like 12 students are exact.

Exam Tip: Exact numbers do not limit precision.

NEET MCQ 10

Question: A repeated close set of readings away from true value is

(a) precise but inaccurate(b) accurate and precise(c) accurate not precise(d) neither

Correct Answer: precise but inaccurate

Explanation: Close readings mean precision; away from truth means inaccurate.

Exam Tip: Target board logic.

NEET MCQ 11

Question: Least count of a metre scale usually is

(a) 1 mm(b) 1 cm(c) 1 m(d) 10 cm

Correct Answer: 1 mm

Explanation: Smallest division on common metre scale is 1 mm.

Exam Tip: Know common least counts.

NEET MCQ 12

Question: Accuracy means closeness to

(a) true value(b) repeated values(c) zero(d) large value

Correct Answer: true value

Explanation: Accuracy compares measured value with true value.

Exam Tip: Accuracy = true value closeness.

NEET MCQ 13

Question: Precision means

(a) repeatability(b) true value closeness(c) large error(d) wrong unit

Correct Answer: repeatability

Explanation: Precision is closeness of repeated readings.

Exam Tip: Precision = reproducibility.

NEET MCQ 14

Question: Number of significant figures in 0.00450 is

(a) 3(b) 2(c) 5(d) 1

Correct Answer: 3

Explanation: Leading zeros are not significant; 4, 5 and final 0 count.

Exam Tip: Leading zeros do not count.

NEET MCQ 15

Question: Number of significant figures in 2.300 is

(a) 4(b) 2(c) 3(d) 1

Correct Answer: 4

Explanation: Trailing zeros after decimal are significant.

Exam Tip: Zeros after decimal count.

NEET MCQ 16

Question: Scientific notation of 0.00072 is

(a) 7.2 × 10-4(b) 72 × 10-5(c) 0.72 × 10-3(d) 7.2 × 104

Correct Answer: 7.2 × 10-4

Explanation: Move decimal four places to right.

Exam Tip: Coefficient must be 1 to 10.

NEET MCQ 17

Question: In addition, final answer follows

(a) least decimal places(b) most significant figures(c) least power(d) largest unit

Correct Answer: least decimal places

Explanation: Addition/subtraction depends on decimal places.

Exam Tip: Decimal place rule.

NEET MCQ 18

Question: In multiplication, final answer follows

(a) least significant figures(b) least decimal places(c) highest value(d) SI prefix

Correct Answer: least significant figures

Explanation: Multiplication/division depends on significant figures.

Exam Tip: Significant figure rule.

NEET MCQ 19

Question: Exact numbers have

(a) infinite significant figures(b) zero significant figures(c) one significant figure(d) two significant figures

Correct Answer: infinite significant figures

Explanation: Counting numbers like 12 students are exact.

Exam Tip: Exact numbers do not limit precision.

NEET MCQ 20

Question: A repeated close set of readings away from true value is

(a) precise but inaccurate(b) accurate and precise(c) accurate not precise(d) neither

Correct Answer: precise but inaccurate

Explanation: Close readings mean precision; away from truth means inaccurate.

Exam Tip: Target board logic.

NEET MCQ 21

Question: Least count of a metre scale usually is

(a) 1 mm(b) 1 cm(c) 1 m(d) 10 cm

Correct Answer: 1 mm

Explanation: Smallest division on common metre scale is 1 mm.

Exam Tip: Know common least counts.

NEET MCQ 22

Question: Accuracy means closeness to

(a) true value(b) repeated values(c) zero(d) large value

Correct Answer: true value

Explanation: Accuracy compares measured value with true value.

Exam Tip: Accuracy = true value closeness.

NEET MCQ 23

Question: Precision means

(a) repeatability(b) true value closeness(c) large error(d) wrong unit

Correct Answer: repeatability

Explanation: Precision is closeness of repeated readings.

Exam Tip: Precision = reproducibility.

NEET MCQ 24

Question: Number of significant figures in 0.00450 is

(a) 3(b) 2(c) 5(d) 1

Correct Answer: 3

Explanation: Leading zeros are not significant; 4, 5 and final 0 count.

Exam Tip: Leading zeros do not count.

NEET MCQ 25

Question: Number of significant figures in 2.300 is

(a) 4(b) 2(c) 3(d) 1

Correct Answer: 4

Explanation: Trailing zeros after decimal are significant.

Exam Tip: Zeros after decimal count.

NEET MCQ 26

Question: Scientific notation of 0.00072 is

(a) 7.2 × 10-4(b) 72 × 10-5(c) 0.72 × 10-3(d) 7.2 × 104

Correct Answer: 7.2 × 10-4

Explanation: Move decimal four places to right.

Exam Tip: Coefficient must be 1 to 10.

NEET MCQ 27

Question: In addition, final answer follows

(a) least decimal places(b) most significant figures(c) least power(d) largest unit

Correct Answer: least decimal places

Explanation: Addition/subtraction depends on decimal places.

Exam Tip: Decimal place rule.

NEET MCQ 28

Question: In multiplication, final answer follows

(a) least significant figures(b) least decimal places(c) highest value(d) SI prefix

Correct Answer: least significant figures

Explanation: Multiplication/division depends on significant figures.

Exam Tip: Significant figure rule.

NEET MCQ 29

Question: Exact numbers have

(a) infinite significant figures(b) zero significant figures(c) one significant figure(d) two significant figures

Correct Answer: infinite significant figures

Explanation: Counting numbers like 12 students are exact.

Exam Tip: Exact numbers do not limit precision.

NEET MCQ 30

Question: A repeated close set of readings away from true value is

(a) precise but inaccurate(b) accurate and precise(c) accurate not precise(d) neither

Correct Answer: precise but inaccurate

Explanation: Close readings mean precision; away from truth means inaccurate.

Exam Tip: Target board logic.

NEET MCQ 31

Question: Least count of a metre scale usually is

(a) 1 mm(b) 1 cm(c) 1 m(d) 10 cm

Correct Answer: 1 mm

Explanation: Smallest division on common metre scale is 1 mm.

Exam Tip: Know common least counts.

NEET MCQ 32

Question: Accuracy means closeness to

(a) true value(b) repeated values(c) zero(d) large value

Correct Answer: true value

Explanation: Accuracy compares measured value with true value.

Exam Tip: Accuracy = true value closeness.

NEET MCQ 33

Question: Precision means

(a) repeatability(b) true value closeness(c) large error(d) wrong unit

Correct Answer: repeatability

Explanation: Precision is closeness of repeated readings.

Exam Tip: Precision = reproducibility.

NEET MCQ 34

Question: Number of significant figures in 0.00450 is

(a) 3(b) 2(c) 5(d) 1

Correct Answer: 3

Explanation: Leading zeros are not significant; 4, 5 and final 0 count.

Exam Tip: Leading zeros do not count.

NEET MCQ 35

Question: Number of significant figures in 2.300 is

(a) 4(b) 2(c) 3(d) 1

Correct Answer: 4

Explanation: Trailing zeros after decimal are significant.

Exam Tip: Zeros after decimal count.

NEET MCQ 36

Question: Scientific notation of 0.00072 is

(a) 7.2 × 10-4(b) 72 × 10-5(c) 0.72 × 10-3(d) 7.2 × 104

Correct Answer: 7.2 × 10-4

Explanation: Move decimal four places to right.

Exam Tip: Coefficient must be 1 to 10.

NEET MCQ 37

Question: In addition, final answer follows

(a) least decimal places(b) most significant figures(c) least power(d) largest unit

Correct Answer: least decimal places

Explanation: Addition/subtraction depends on decimal places.

Exam Tip: Decimal place rule.

NEET MCQ 38

Question: In multiplication, final answer follows

(a) least significant figures(b) least decimal places(c) highest value(d) SI prefix

Correct Answer: least significant figures

Explanation: Multiplication/division depends on significant figures.

Exam Tip: Significant figure rule.

NEET MCQ 39

Question: Exact numbers have

(a) infinite significant figures(b) zero significant figures(c) one significant figure(d) two significant figures

Correct Answer: infinite significant figures

Explanation: Counting numbers like 12 students are exact.

Exam Tip: Exact numbers do not limit precision.

NEET MCQ 40

Question: A repeated close set of readings away from true value is

(a) precise but inaccurate(b) accurate and precise(c) accurate not precise(d) neither

Correct Answer: precise but inaccurate

Explanation: Close readings mean precision; away from truth means inaccurate.

Exam Tip: Target board logic.

NEET MCQ 41

Question: Least count of a metre scale usually is

(a) 1 mm(b) 1 cm(c) 1 m(d) 10 cm

Correct Answer: 1 mm

Explanation: Smallest division on common metre scale is 1 mm.

Exam Tip: Know common least counts.

NEET MCQ 42

Question: Accuracy means closeness to

(a) true value(b) repeated values(c) zero(d) large value

Correct Answer: true value

Explanation: Accuracy compares measured value with true value.

Exam Tip: Accuracy = true value closeness.

NEET MCQ 43

Question: Precision means

(a) repeatability(b) true value closeness(c) large error(d) wrong unit

Correct Answer: repeatability

Explanation: Precision is closeness of repeated readings.

Exam Tip: Precision = reproducibility.

NEET MCQ 44

Question: Number of significant figures in 0.00450 is

(a) 3(b) 2(c) 5(d) 1

Correct Answer: 3

Explanation: Leading zeros are not significant; 4, 5 and final 0 count.

Exam Tip: Leading zeros do not count.

NEET MCQ 45

Question: Number of significant figures in 2.300 is

(a) 4(b) 2(c) 3(d) 1

Correct Answer: 4

Explanation: Trailing zeros after decimal are significant.

Exam Tip: Zeros after decimal count.

NEET MCQ 46

Question: Scientific notation of 0.00072 is

(a) 7.2 × 10-4(b) 72 × 10-5(c) 0.72 × 10-3(d) 7.2 × 104

Correct Answer: 7.2 × 10-4

Explanation: Move decimal four places to right.

Exam Tip: Coefficient must be 1 to 10.

NEET MCQ 47

Question: In addition, final answer follows

(a) least decimal places(b) most significant figures(c) least power(d) largest unit

Correct Answer: least decimal places

Explanation: Addition/subtraction depends on decimal places.

Exam Tip: Decimal place rule.

NEET MCQ 48

Question: In multiplication, final answer follows

(a) least significant figures(b) least decimal places(c) highest value(d) SI prefix

Correct Answer: least significant figures

Explanation: Multiplication/division depends on significant figures.

Exam Tip: Significant figure rule.

NEET MCQ 49

Question: Exact numbers have

(a) infinite significant figures(b) zero significant figures(c) one significant figure(d) two significant figures

Correct Answer: infinite significant figures

Explanation: Counting numbers like 12 students are exact.

Exam Tip: Exact numbers do not limit precision.

NEET MCQ 50

Question: A repeated close set of readings away from true value is

(a) precise but inaccurate(b) accurate and precise(c) accurate not precise(d) neither

Correct Answer: precise but inaccurate

Explanation: Close readings mean precision; away from truth means inaccurate.

Exam Tip: Target board logic.

NEET MCQ 51

Question: Least count of a metre scale usually is

(a) 1 mm(b) 1 cm(c) 1 m(d) 10 cm

Correct Answer: 1 mm

Explanation: Smallest division on common metre scale is 1 mm.

Exam Tip: Know common least counts.

NEET MCQ 52

Question: Accuracy means closeness to

(a) true value(b) repeated values(c) zero(d) large value

Correct Answer: true value

Explanation: Accuracy compares measured value with true value.

Exam Tip: Accuracy = true value closeness.

NEET MCQ 53

Question: Precision means

(a) repeatability(b) true value closeness(c) large error(d) wrong unit

Correct Answer: repeatability

Explanation: Precision is closeness of repeated readings.

Exam Tip: Precision = reproducibility.

NEET MCQ 54

Question: Number of significant figures in 0.00450 is

(a) 3(b) 2(c) 5(d) 1

Correct Answer: 3

Explanation: Leading zeros are not significant; 4, 5 and final 0 count.

Exam Tip: Leading zeros do not count.

NEET MCQ 55

Question: Number of significant figures in 2.300 is

(a) 4(b) 2(c) 3(d) 1

Correct Answer: 4

Explanation: Trailing zeros after decimal are significant.

Exam Tip: Zeros after decimal count.

NEET MCQ 56

Question: Scientific notation of 0.00072 is

(a) 7.2 × 10-4(b) 72 × 10-5(c) 0.72 × 10-3(d) 7.2 × 104

Correct Answer: 7.2 × 10-4

Explanation: Move decimal four places to right.

Exam Tip: Coefficient must be 1 to 10.

NEET MCQ 57

Question: In addition, final answer follows

(a) least decimal places(b) most significant figures(c) least power(d) largest unit

Correct Answer: least decimal places

Explanation: Addition/subtraction depends on decimal places.

Exam Tip: Decimal place rule.

NEET MCQ 58

Question: In multiplication, final answer follows

(a) least significant figures(b) least decimal places(c) highest value(d) SI prefix

Correct Answer: least significant figures

Explanation: Multiplication/division depends on significant figures.

Exam Tip: Significant figure rule.

NEET MCQ 59

Question: Exact numbers have

(a) infinite significant figures(b) zero significant figures(c) one significant figure(d) two significant figures

Correct Answer: infinite significant figures

Explanation: Counting numbers like 12 students are exact.

Exam Tip: Exact numbers do not limit precision.

NEET MCQ 60

Question: A repeated close set of readings away from true value is

(a) precise but inaccurate(b) accurate and precise(c) accurate not precise(d) neither

Correct Answer: precise but inaccurate

Explanation: Close readings mean precision; away from truth means inaccurate.

Exam Tip: Target board logic.

13. JEE Main Question Bank

JEE Main Numerical

Question: Round 12.11 + 18.0 + 1.013 correctly.

Solution: Raw sum = 31.123. Least decimal places is 1, so answer = 31.1.

Final Answer: 31.1

Exam Tip: Use decimal-place rule.

JEE Main Conceptual

Question: Why does multiplication use significant figures instead of decimal places?

Solution: Multiplication uncertainty depends on relative precision of factors.

Final Answer: Use least significant figures.

Exam Tip: Remember operation-specific rule.

JEE Main Multiple Correct

Question: Which are significant in 0.02030?

Solution: 2, 0 between 2 and 3, 3 and final 0 after decimal are significant.

Final Answer: 4 significant figures

Exam Tip: Leading zeros are ignored.

JEE Main Reasoning

Question: A precise instrument may still give inaccurate readings. Why?

Solution: Systematic error can shift all readings away from true value.

Final Answer: Precision does not guarantee accuracy.

Exam Tip: Think target board.

14. JEE Advanced Conceptual Questions

Advanced Concept 1

Question: Can an answer have more significant figures than the least precise data?

Solution: No, it would imply false precision.

Final Answer: No.

Exam Tip: Report realistically.

Advanced Concept 2

Question: Why are exact numbers treated as infinite significant figures?

Solution: They are counted or defined, not measured.

Final Answer: They do not limit significant figures.

Exam Tip: Exact numbers are not uncertain.

Advanced Concept 3

Question: A measurement is reproducible but biased. Interpret it.

Solution: It is precise but inaccurate due to systematic error.

Final Answer: Precise but not accurate.

Exam Tip: Bias means accuracy issue.

Advanced Concept 4

Question: Why is scientific notation useful in error reporting?

Solution: It clearly shows significant figures and powers of ten.

Final Answer: It improves clarity.

Exam Tip: Coefficient shows SF.

15. CBSE School Exam Questions

1 Mark

Question: Define least count.

Solution: Smallest value measurable by an instrument.

Final Answer: Least count definition.

Exam Tip: Write concise.

2 Mark

Question: Differentiate accuracy and precision.

Solution: Accuracy is true-value closeness; precision is repeatability.

Final Answer: Both are different.

Exam Tip: Use table if possible.

3 Mark

Question: Explain rules for significant figures with examples.

Solution: Leading zeros not significant, captive zeros significant, trailing decimal zeros significant.

Final Answer: Use examples 0.00450 and 2.300.

Exam Tip: Examples score marks.

5 Mark

Question: Explain measurement, least count, accuracy, precision and significant figures.

Solution: Measurement compares with standard unit; least count is smallest measurable value; accuracy and precision judge quality; significant figures report precision.

Final Answer: Complete answer.

Exam Tip: Write headings.

16. IB Physics Questions

IB 1

Question: Why is uncertainty important in experimental physics?

Solution: It states the reliability and range of possible true values.

Final Answer: Uncertainty qualifies measurement.

Exam Tip: IB values uncertainty language.

IB 2

Question: How should repeated measurements be reported?

Solution: Use mean value with appropriate uncertainty and significant figures.

Final Answer: Mean with uncertainty.

Exam Tip: Mention repeats.

IB 3

Question: Why should final answer not contain too many digits?

Solution: Extra digits imply unsupported precision.

Final Answer: Use significant figures.

Exam Tip: Avoid calculator dump.

17. IGCSE Physics Questions

IGCSE 1

Question: Why use a measuring cylinder at eye level?

Solution: To avoid parallax error.

Final Answer: Avoid parallax.

Exam Tip: Eye-level reading.

IGCSE 2

Question: What is precision?

Solution: Closeness of repeated readings.

Final Answer: Repeatability.

Exam Tip: Short definition.

IGCSE 3

Question: Convert 0.00045 to scientific notation.

Solution: 4.5 × 10-4.

Final Answer: 4.5 × 10-4.

Exam Tip: Move decimal.

18. A-Level Questions

A-Level 1

Question: Explain how least count affects measurement uncertainty.

Solution: Smaller least count generally reduces instrument resolution uncertainty.

Final Answer: Smaller least count improves resolution.

Exam Tip: Do not confuse with systematic error.

A-Level 2

Question: Why are significant figures linked to measurement quality?

Solution: They show meaningful precision supported by data.

Final Answer: SF reflects precision.

Exam Tip: Tie digits to uncertainty.

A-Level 3

Question: A value is reported as 3.00 × 108. What does 3.00 show?

Solution: It shows three significant figures.

Final Answer: 3 SF.

Exam Tip: Trailing decimal zeros count.

19. Assertion Reason Questions

Assertion Reason 1

Assertion: Least count is the smallest value measurable by an instrument.

Reason: A smaller least count usually gives more precise measurement.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 2

Assertion: Trailing zeros after decimal are significant.

Reason: They show measurement precision.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 3

Assertion: Leading zeros are significant.

Reason: Leading zeros only locate decimal point.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion is false and reason is true.

Assertion Reason 4

Assertion: Accuracy and precision are identical.

Reason: Accuracy means closeness to true value.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion is false; reason is true.

Assertion Reason 5

Assertion: In multiplication, answer uses least significant figures.

Reason: Multiplication uncertainty depends on relative precision.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct rule and explanation.

Assertion Reason 6

Assertion: In addition, answer uses least decimal places.

Reason: Addition uncertainty depends on absolute place value.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct rule and explanation.

Assertion Reason 7

Assertion: Scientific notation helps express very large and small numbers.

Reason: It uses powers of ten.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct explanation.

Assertion Reason 8

Assertion: Exact numbers limit significant figures.

Reason: Exact counted numbers have no measurement uncertainty.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion false; reason true.

Assertion Reason 9

Assertion: Screw gauge can measure small thickness accurately.

Reason: It has small least count.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct explanation.

Assertion Reason 10

Assertion: Random error is removed completely by one reading.

Reason: Repeated readings reduce random error.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion false; reason true.

Assertion Reason 11

Assertion: Least count is the smallest value measurable by an instrument.

Reason: A smaller least count usually gives more precise measurement.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 12

Assertion: Trailing zeros after decimal are significant.

Reason: They show measurement precision.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 13

Assertion: Leading zeros are significant.

Reason: Leading zeros only locate decimal point.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion is false and reason is true.

Assertion Reason 14

Assertion: Accuracy and precision are identical.

Reason: Accuracy means closeness to true value.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion is false; reason is true.

Assertion Reason 15

Assertion: In multiplication, answer uses least significant figures.

Reason: Multiplication uncertainty depends on relative precision.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct rule and explanation.

Assertion Reason 16

Assertion: In addition, answer uses least decimal places.

Reason: Addition uncertainty depends on absolute place value.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct rule and explanation.

Assertion Reason 17

Assertion: Scientific notation helps express very large and small numbers.

Reason: It uses powers of ten.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct explanation.

Assertion Reason 18

Assertion: Exact numbers limit significant figures.

Reason: Exact counted numbers have no measurement uncertainty.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion false; reason true.

Assertion Reason 19

Assertion: Screw gauge can measure small thickness accurately.

Reason: It has small least count.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct explanation.

Assertion Reason 20

Assertion: Random error is removed completely by one reading.

Reason: Repeated readings reduce random error.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion false; reason true.

Assertion Reason 21

Assertion: Least count is the smallest value measurable by an instrument.

Reason: A smaller least count usually gives more precise measurement.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 22

Assertion: Trailing zeros after decimal are significant.

Reason: They show measurement precision.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Both are true and reason explains assertion.

Assertion Reason 23

Assertion: Leading zeros are significant.

Reason: Leading zeros only locate decimal point.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion is false and reason is true.

Assertion Reason 24

Assertion: Accuracy and precision are identical.

Reason: Accuracy means closeness to true value.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion is false; reason is true.

Assertion Reason 25

Assertion: In multiplication, answer uses least significant figures.

Reason: Multiplication uncertainty depends on relative precision.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct rule and explanation.

Assertion Reason 26

Assertion: In addition, answer uses least decimal places.

Reason: Addition uncertainty depends on absolute place value.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct rule and explanation.

Assertion Reason 27

Assertion: Scientific notation helps express very large and small numbers.

Reason: It uses powers of ten.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct explanation.

Assertion Reason 28

Assertion: Exact numbers limit significant figures.

Reason: Exact counted numbers have no measurement uncertainty.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion false; reason true.

Assertion Reason 29

Assertion: Screw gauge can measure small thickness accurately.

Reason: It has small least count.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (a)

Explanation: Correct explanation.

Assertion Reason 30

Assertion: Random error is removed completely by one reading.

Reason: Repeated readings reduce random error.

Options: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Answer: (d)

Explanation: Assertion false; reason true.

20. Case Study Questions

Case Study: Vernier Calipers

A student measures the diameter of a cylinder using vernier calipers. The instrument has a small least count and reduces reading uncertainty compared with a ruler.

Questions: 1. What is measured? 2. Why use vernier? 3. What does least count mean? 4. Is careful reading needed?

Answers: Diameter; smaller least count; smallest measurable value; yes, to avoid observational errors.

Explanation: The case connects measurement quality with significant figures and instrument choice.

Case Study: Screw Gauge

A screw gauge is used to measure the diameter of a thin wire. It uses rotation and pitch to measure small lengths.

Questions: 1. What is measured? 2. Why not use ruler? 3. Which instrument is better for wire? 4. What error must be checked?

Answers: Wire diameter; ruler least count is large; screw gauge; zero error.

Explanation: The case connects measurement quality with significant figures and instrument choice.

Case Study: Significant Figures

A value is reported as 0.00450 m. Leading zeros locate decimal point while final zero after decimal shows precision.

Questions: 1. How many significant figures? 2. Are leading zeros significant? 3. Is final zero significant? 4. Why?

Answers: 3; no; yes; trailing decimal zero shows precision.

Explanation: The case connects measurement quality with significant figures and instrument choice.

Case Study: Scientific Measurements

In a lab, students repeat measurements and report average with correct units and significant figures.

Questions: 1. Why repeat readings? 2. Why average? 3. Why units? 4. Why SF?

Answers: Reduce random error; improve reliability; value needs meaning; show precision.

Explanation: The case connects measurement quality with significant figures and instrument choice.

Case Study: Experimental Accuracy

A voltmeter has zero error, so all readings are shifted by the same amount. Repeated readings are close.

Questions: 1. Error type? 2. Are readings precise? 3. Are readings accurate? 4. How to correct?

Answers: Systematic error; yes; no; calibrate or subtract zero error.

Explanation: The case connects measurement quality with significant figures and instrument choice.

21. Quick Revision Notes

One Page Revision Sheet

  • Measurement = numerical value + unit
  • Least count = smallest measurable value
  • Accuracy = closeness to true value
  • Precision = repeatability

Significant Figure Rules

  • Non-zero digits are significant
  • Leading zeros are not significant
  • Captive zeros are significant
  • Trailing decimal zeros are significant

Common Mistakes

  • Writing too many calculator digits
  • Confusing decimal places with significant figures
  • Ignoring exact numbers
  • Confusing accuracy and precision
Exam tips: For addition/subtraction use decimal places. For multiplication/division use significant figures. Always write units and avoid unsupported extra digits.
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