Significant Figures Rules Quiz: Master Measurement Skills

1. 3.0 − 1.27 should be rounded to one decimal place.

True

False

Concept: subtraction decimal-place rule. 3.0 is to one decimal place; 1.27 is to two. The result must be to one decimal place.

Explanation

Concept: subtraction decimal-place rule. 3.0 is to one decimal place; 1.27 is to two. The result must be to one decimal place.

2. The best overall summary of calculation rules is:

Always round to 2 sig figs no matter what

Multiply/divide → fewest sig figs; add/subtract → fewest decimal places

Add/subtract → fewest sig figs; multiply/divide → fewest decimals

Never round any answer

Concept: standard sig-fig rules. Different operations limit precision in different ways. Following the correct rule keeps results consistent with measurement limits.

Explanation

Concept: standard sig-fig rules. Different operations limit precision in different ways. Following the correct rule keeps results consistent with measurement limits.

3. In scientific notation, rounding is easier because sig figs are clear in the coefficient.

True

False

Concept: scientific notation advantage. You round the coefficient to the required digits. The power of ten stays the same (or adjusts if rounding changes the coefficient).

Explanation

Concept: scientific notation advantage. You round the coefficient to the required digits. The power of ten stays the same (or adjusts if rounding changes the coefficient).

4. When rounding to significant figures, you ignore leading zeros while counting.

True

False

Concept: leading zeros don’t count. They only place the decimal point. Sig-fig counting begins at the first non-zero digit.

Explanation

Concept: leading zeros don’t count. They only place the decimal point. Sig-fig counting begins at the first non-zero digit.

5. Rounding 19.96 to 3 significant figures gives:

19.9

20.0

19.96

19.0

Concept: carrying in rounding. The first three sig figs are 1, 9, 9; the next digit is 6 so you round up. 19.9 becomes 20.0 to keep 3 sig figs.

Explanation

Concept: carrying in rounding. The first three sig figs are 1, 9, 9; the next digit is 6 so you round up. 19.9 becomes 20.0 to keep 3 sig figs.

6. 3.0 − 1.27 = (correct rounding):

1.73

1.7

1.70

2

Concept: decimal place limitation. Exact subtraction gives 1.73. Rounded to one decimal place → 1.7.

Explanation

Concept: decimal place limitation. Exact subtraction gives 1.73. Rounded to one decimal place → 1.7.

7. Writing results in scientific notation can remove ambiguity about how many significant figures you intend.

True

False

Concept: clarity of intent. Scientific notation makes the significant digits explicit in the coefficient. This is especially helpful with trailing zeros.

Explanation

Concept: clarity of intent. Scientific notation makes the significant digits explicit in the coefficient. This is especially helpful with trailing zeros.

8. 6.2 ÷ 0.31 = 20 (exact calculator gives 20). Correct sig figs is:

2.0 × 10¹ (2 sig figs)

2.0 × 10¹

20.0

2 × 10¹ only

Concept: division sig figs. 6.2 has 2 sig figs, 0.31 has 2 sig figs, so answer has 2 sig figs. '2.0 × 10¹' clearly shows 2 sig figs.

Explanation

Concept: division sig figs. 6.2 has 2 sig figs, 0.31 has 2 sig figs, so answer has 2 sig figs. '2.0 × 10¹' clearly shows 2 sig figs.

9. A calculator display showing many digits does not mean the result is physically that precise.

True

False

Concept: avoid false precision. Calculators show numerical output, not measurement uncertainty. You must round based on input precision rules.

Explanation

Concept: avoid false precision. Calculators show numerical output, not measurement uncertainty. You must round based on input precision rules.

10. The rule for addition/subtraction uses the least precise ______ place.

Concept: place-value alignment. Add/subtract depends on aligning decimals. The least precise decimal place sets how far you can trust the result.

Explanation

Concept: place-value alignment. Add/subtract depends on aligning decimals. The least precise decimal place sets how far you can trust the result.

Submit

11. (2.50 × 10²) + (1.2 × 10²) = (correct rounding, written in normal form):

370

3.70 × 10² (too precise?)

3.7 × 10² only

Concept: addition and place value. 2.50×10² = 250 (to ones), 1.2×10² = 120 (to tens). Sum is 370, rounded to tens → 370 (i.e., 3.7×10²).

Explanation

Concept: addition and place value. 2.50×10² = 250 (to ones), 1.2×10² = 120 (to tens). Sum is 370, rounded to tens → 370 (i.e., 3.7×10²).

12. Rounding 0.00999 to 2 significant figures gives:

0.0099

0.009

0.010

0.01 (with 1 sig fig)

Concept: rounding with carry and sig figs. The first two sig digits are 9 and 9; the next digit would round up. 0.00999 becomes 0.010, which shows 2 sig figs (1 and 0).

Explanation

Concept: rounding with carry and sig figs. The first two sig digits are 9 and 9; the next digit would round up. 0.00999 becomes 0.010, which shows 2 sig figs (1 and 0).

13. It’s best to keep extra digits during intermediate steps and round only at the end.

True

False

Concept: avoiding round-off error. Rounding too early can accumulate error. Keep guard digits, then round final results to the correct precision.

Explanation

Concept: avoiding round-off error. Rounding too early can accumulate error. Keep guard digits, then round final results to the correct precision.

14. 12.3 + 0.45 = (with correct rounding):

12.75

12.8

12.70

13

Concept: addition rounding. 12.3 is precise to the tenths place, while 0.45 is to the hundredths. The sum is 12.75, rounded to tenths → 12.8.

Explanation

Concept: addition rounding. 12.3 is precise to the tenths place, while 0.45 is to the hundredths. The sum is 12.75, rounded to tenths → 12.8.

15. For addition/subtraction, you round based on the least number of decimal places (not sig figs).

True

False

Concept: add/subtract decimal-place rule. Adding and subtracting aligns place values. The measurement with the fewest decimal places limits the final decimal place.

Explanation

Concept: add/subtract decimal-place rule. Adding and subtracting aligns place values. The measurement with the fewest decimal places limits the final decimal place.

16. In multiplication/division, the result should have the same number of significant figures as the factor with the ______ sig figs.

Concept: multiplication/division rule. The least-precise measurement limits the precision of the product or quotient. This avoids reporting more precision than the inputs justify.

Explanation

Concept: multiplication/division rule. The least-precise measurement limits the precision of the product or quotient. This avoids reporting more precision than the inputs justify.

Submit

17. Rounding 0.012345 to 3 significant figures gives:

0.012

0.0123

0.01235

0.01234

Concept: rounding to sig figs. Count from the first non-zero digit: 1 (1st), 2 (2nd), 3 (3rd). The next digit is 4, so you keep 0.0123.

Explanation

Concept: rounding to sig figs. Count from the first non-zero digit: 1 (1st), 2 (2nd), 3 (3rd). The next digit is 4, so you keep 0.0123.

18. 4.56 × 1.4 = (correct sig figs):

6.384

6.38

6.4

6

Concept: multiplication sig figs. 4.56 has 3 sig figs, 1.4 has 2 sig figs, so the result must have 2 sig figs. 6.384 rounds to 6.4.

Explanation

Concept: multiplication sig figs. 4.56 has 3 sig figs, 1.4 has 2 sig figs, so the result must have 2 sig figs. 6.384 rounds to 6.4.

19. 25 written as 25.0 has ______ significant figures.

Concept: decimal makes zeros significant. The trailing zero after the decimal is significant. So 25.0 has three significant figures.

Explanation

Concept: decimal makes zeros significant. The trailing zero after the decimal is significant. So 25.0 has three significant figures.

Submit

20. 100.0 ÷ 4.0 = (correct sig figs):

25

25.0

25

25.00

Concept: sig figs in division. 100.0 has 4 sig figs, 4.0 has 2 sig figs, so answer has 2 sig figs. 25 is 2 sig figs.

Explanation

Concept: sig figs in division. 100.0 has 4 sig figs, 4.0 has 2 sig figs, so answer has 2 sig figs. 25 is 2 sig figs.

Significant Figures Rules Quiz: Test Your Measurement Skills

1. 3.0 − 1.27 should be rounded to one decimal place.

2.

What first name or nickname would you like us to use?

2. The best overall summary of calculation rules is:

3. In scientific notation, rounding is easier because sig figs are clear in the coefficient.

4. When rounding to significant figures, you ignore leading zeros while counting.

5. Rounding 19.96 to 3 significant figures gives:

6. 3.0 − 1.27 = (correct rounding):

7. Writing results in scientific notation can remove ambiguity about how many significant figures you intend.

8. 6.2 ÷ 0.31 = 20 (exact calculator gives 20). Correct sig figs is:

9. A calculator display showing many digits does not mean the result is physically that precise.

10. The rule for addition/subtraction uses the least precise ______ place.

11. (2.50 × 10²) + (1.2 × 10²) = (correct rounding, written in normal form):

12. Rounding 0.00999 to 2 significant figures gives:

13. It’s best to keep extra digits during intermediate steps and round only at the end.

14. 12.3 + 0.45 = (with correct rounding):

15. For addition/subtraction, you round based on the least number of decimal places (not sig figs).

16. In multiplication/division, the result should have the same number of significant figures as the factor with the ______ sig figs.

17. Rounding 0.012345 to 3 significant figures gives:

18. 4.56 × 1.4 = (correct sig figs):

19. 25 written as 25.0 has ______ significant figures.

20. 100.0 ÷ 4.0 = (correct sig figs):