Significant Figures Flashcards: Mixed Operations & Rounding

Question 1

In introductory significant-figure arithmetic, which reporting limit governs adding or subtracting measured values in compatible units?

Accepted Answer

The coarsest last reported place among the inputs

Track a decimal place, such as tenths or hundredths, rather than taking the smallest significant-figure count.

Question 2

Which reporting limit governs multiplying or dividing measured values under introductory significant-figure rules?

Accepted Answer

The smallest significant-figure count among the measured inputs

An explicitly exact count or defined factor does not impose a finite count limit.

Question 3

A measured value is written as 0.0460. How many significant figures does that notation retain?

Accepted Answer

Three

The leading zeros locate the decimal point. The final zero retains the ten-thousandths place; it is significant.

Question 4

Exactly 8 identical portions are counted. Does that count restrict a calculation to one significant figure?

Accepted Answer

No

An exact count has no finite significant-figure limit. Measured quantities still constrain the result.

Question 5

What two records should you keep for an intermediate result in a mixed-operation significant-figure calculation?

Accepted Answer

Its unrounded carried value and its reporting limit

Use the carried value in the next calculation. Keep the allowed count or decimal place separately, and round only the final report.

Question 6

At a change from addition to multiplication, how do you find the intermediate sum’s significant-figure count without rounding the value you carry?

Accepted Answer

Count the digits in its reportable form at the sum’s allowed place

That form determines the next count limit; the unrounded sum remains the numerical input. Extra calculator digits do not add measured precision.

Question 7

Report (8.4 + 2.17) × 3.62 using introductory significant-figure rules. These are measured inputs in an abstract arithmetic exercise; units are omitted.

Accepted Answer

38.3

Carry the sum 10.57 and product 38.2634. The sum is limited to tenths (reportable as 10.6, three figures); 3.62 also has three figures, so report three.

Question 8

Report 2.46 × 3.1 + 0.842. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

8.5

Carry the product 7.626 and sum 8.468. The product has a two-figure limit (7.6), whose last place is tenths. That is coarser than the addend’s thousandths, so the final sum ends at tenths.

Question 9

A measured sum is carried as 0.0827 with a thousandths reporting limit. How many figures may that sum contribute to a following multiplication?

Accepted Answer

Two

Its reportable form is 0.083. Use that two-figure limit while carrying 0.0827 numerically.

Question 10

Report (15.83 − 4.2) ÷ 2.74. Use introductory significant-figure rules; inputs are measured and units are omitted for this abstract exercise.

Accepted Answer

4.24

Carry 11.63 through the division: 11.63/2.74 = 4.244525547…. The difference has a tenths limit (11.6, three figures); the divisor has three figures. Report three.

Question 11

A calculated measured result is correctly reported as 12.30 under significant-figure rules. Does that notation establish that it is close to the true value?

Accepted Answer

No

It states a reporting limit, here four figures ending at hundredths. Accuracy needs evidence about the measurement and a suitable reference; retained digits alone do not provide it.

Question 12

For (2.8 + 0.146) × 6.63, a student substitutes 2.9 for the sum and reports 1.9 × 10¹. What final report follows from carrying the unrounded sum? Use introductory rules; measured abstract inputs, units omitted.

Accepted Answer

2.0 × 10¹

Carry 2.946, giving 19.53198. The sum has a tenths limit (2.9, two figures), so the final report has two figures. Substituting 2.9 early changes the carried product to 19.227 and changes the final rounding.

Question 13

Report 0.0374 × 2.6 + 0.00418. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

0.101

Carry product 0.09724 and sum 0.10142. The product’s two-figure form is 0.097, ending at thousandths. The final addition uses that place, even though 0.101 has three figures.

Question 14

A measured product is carried as 63.784 with a three-figure reporting limit. What last place does it contribute to a following addition?

Accepted Answer

Tenths

Its three-figure form is 63.8. Keep 63.784 in the numerical calculation; use tenths in the addition’s limit ledger.

Question 15

Report (6.28 − 5.9) × 7.43. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

3

The difference is carried as 0.38, with a tenths limit (reportable as 0.4, one figure). The unrounded product is 2.8234; its one-figure limit gives 3.

Question 16

Report (6.27 + 0.46) ÷ 3, where 3 is an explicitly exact defined divisor and the other inputs are measured. Use introductory rules; abstract arithmetic, units omitted.

Accepted Answer

2.24

Carry sum 6.73 and quotient 2.243333333…. The sum’s hundredths limit gives three figures. The exact divisor imposes no finite limit, so retain three.

Question 17

Report 18.24 ÷ 4.2 − 0.316. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

4.0

Carry the quotient 4.342857142… and difference 4.026857142…. Two figures make the quotient reportable as 4.3, ending at tenths. The subtraction therefore ends at tenths; keep the zero in 4.0.

Question 18

A student reports 3.26 × 1.7 + 0.024 as 5.566. What final report corrects the excess digits? Use introductory rules; measured abstract inputs, units omitted.

Accepted Answer

5.6

Carry product 5.542 and sum 5.566. The product is limited to two figures (5.5, tenths), so the final addition ends at tenths.

Question 19

A student assigns two significant figures to (14.2 − 0.87) × 2.36 by choosing the smallest count anywhere in the expression. What final figure count should replace that choice? Use introductory rules; measured abstract inputs, units omitted.

Accepted Answer

Three

Carry the difference 13.33 and product 31.4588. Subtraction gives a tenths limit (13.3, three figures), then multiplication uses three figures from each input. The final report is 31.5.

Question 20

Report 7 × (1.83 + 0.4), where 7 is an explicitly exact defined multiplier and the other inputs are measured. Use introductory significant-figure rules; abstract arithmetic, units omitted.

Accepted Answer

1.6 × 10¹

Carry sum 2.23 and product 15.61. The sum has a tenths limit (2.2, two figures). The exact multiplier does not reduce that count, so report two figures.

Question 21

Report 7.82 ÷ 3.46 + 1.7. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

4.0

Carry quotient 2.260115606… and sum 3.960115606…. The quotient’s three-figure form, 2.26, ends at hundredths. The measured addend 1.7 sets the coarser tenths limit.

Question 22

A measured quotient is carried as 0.009974 with a two-figure limit. What last place does it contribute to a following addition?

Accepted Answer

Thousandths

Its two-figure form is 0.010. The last retained zero is in the thousandths place after rounding changes the magnitude; carry 0.009974.

Question 23

For 24.81 + 2.3 × 1.4, a student applies a two-significant-figure limit to the final addition. Which decimal place should govern that addition instead? Use introductory rules; measured abstract inputs, units omitted.

Accepted Answer

Tenths

Carry product 3.22 and sum 28.03. The product’s two-figure form is 3.2, ending at tenths, which is coarser than 24.81’s hundredths. The final report is 28.0.

Question 24

Report (0.0631 + 0.008) × 4.26. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

0.30

Carry the sum 0.0711 and product 0.302886. The sum’s thousandths limit gives 0.071, two figures. The product is therefore limited to two figures; the final zero in 0.30 matters.

Question 25

Report 4 × (2.746 − 0.18), where 4 is an explicitly exact defined multiplier and the other inputs are measured. Use introductory rules; abstract arithmetic, units omitted.

Accepted Answer

10.3

Carry difference 2.566 and product 10.264. The difference has a hundredths limit (2.57, three figures). The exact factor leaves a three-figure final limit.

Question 26

A measured sum is carried as 9.962 with a tenths reporting limit. How many figures does it contribute to a following multiplication?

Accepted Answer

Three

At tenths, its reportable form is 10.0, with three figures. Carry 9.962 rather than replacing it with 10.0.

Question 27

Report (42.6 + 1.384) ÷ 6.237. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

7.05

Carry 43.984 into the quotient, giving 7.052108385…. The sum has a tenths limit: 44.0 retains three figures. The divisor has four, so report three.

Question 28

A student reports 12.83 × 3.2 + 0.274 as 41.3. What final report follows from the product’s proper handoff limit? Use introductory rules; measured abstract inputs, units omitted.

Accepted Answer

41

Carry product 41.056 and sum 41.330. The product has two figures (41), ending at units. The final sum must also end at units.

Question 29

Report 23.4 × 6.1 − 2.38. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

1.4 × 10²

Carry product 142.74 and difference 140.36. The product’s two-figure form is 1.4 × 10², ending at tens. The final subtraction also ends at tens; scientific notation makes that limit clear.

Question 30

Can a significant-figure count alone determine a measured input’s statistical uncertainty distribution?

Accepted Answer

No

These classroom rules approximate how to report digits. An uncertainty model needs measurement information; the count does not specify a distribution or perform uncertainty propagation.

Question 31

Report (1.806 − 0.73) ÷ 0.4821. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

2.23

Carry the difference 1.076; the quotient is 2.231902095…. The difference’s hundredths limit gives 1.08, three figures, which limits the final division.

Question 32

A measured product is carried as 98.76 with a two-figure limit. What last place does it contribute to a following subtraction?

Accepted Answer

Units

Its reportable form is 99. Carry 98.76, but use the units place when comparing the addends’ reporting limits.

Question 33

A student reports 0.028 × 4.316 + 0.0034 as 0.1242, using four calculator digits from the product. What final report corrects that choice? Use introductory rules; measured abstract inputs, units omitted.

Accepted Answer

0.12

Carry product 0.120848 and sum 0.124248. The product has a two-figure limit (0.12), ending at hundredths. That place governs the addition.

Question 34

Measured masses 7.31 g, 8.42 g and 9.16 g are averaged by dividing their sum by an exact count of 3. A student lets that count impose a one-figure limit. What figure count should replace it under the introductory sum-then-division rules?

Accepted Answer

Four

Carry sum 24.89 g and quotient 8.296666666… g. The sum’s hundredths limit gives four figures; the exact divisor adds no limit. These classroom rules give 8.297 g, without supplying a full uncertainty analysis.

Question 35

Report (3.47 + 0.2) ÷ (8.16 − 2.05). Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

0.60

Carry numerator 3.67 and denominator 6.11, giving 0.600654664…. The numerator’s tenths limit gives 3.7 (two figures); the denominator has a hundredths limit and three figures. Report two.

Question 36

Report 0.806 ÷ 2.4 − 0.0127. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

0.32

Carry quotient 0.335833333… and difference 0.323133333…. Two figures give the quotient a hundredths limit (0.34). That sets the final subtraction’s place.

Question 37

A measured sum is carried as 102.04 with a units reporting limit. How many figures does it contribute to a following division?

Accepted Answer

Three

The units-limited form is 102; its internal zero is significant. Carry 102.04 and use a three-figure limit.

Question 38

Report 4.72 × 1.83 + 6.4 × 2.1. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

22

Carry products 8.6376 and 13.44; the sum is 22.0776. Their reportable forms are 8.64 (hundredths) and 13 (units). The final sum ends at units.

Question 39

Report (24.8 − 7.16) × (1.42 + 0.083). Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

26.5

Carry 17.64 and 1.503, whose product is 26.51292. Their limits are tenths (17.6, three figures) and hundredths (1.50, three figures). Report the product with three figures.

Question 40

Report 31.8 ÷ 4.12 − 1.6 × 2.7. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

3.4

Carry quotient 7.718446601… and product 4.32; the difference is 3.398446601…. Their reportable forms end at hundredths (7.72) and tenths (4.3). The final difference ends at tenths.

Question 41

For (9.36 − 8.9) ÷ 0.384, a student enters 0.5 as the numerator after rounding the difference. Which numerical value should be carried as the numerator instead? Use introductory rules; measured abstract inputs, units omitted.

Accepted Answer

0.46

The unrounded difference is 0.46. Keep its tenths limit separately (reportable as 0.5, one figure). Carrying 0.46 gives quotient 1.197916666… and a one-figure final report of 1.

Question 42

Report (2.36 × 10³ + 4.7 × 10²) ÷ 8.214. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

3.45 × 10²

Carry the sum 2830 and quotient 344.533722912…. Both addends end at the tens place, so the sum is reportable as 2.83 × 10³, three figures. The final quotient retains three.

Question 43

Report 1.247 × 8.019 + 0.01234. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

10.01

Carry product 9.999693 and sum 10.012033. The product’s four-figure reportable form is 10.00, ending at hundredths after the magnitude change. That hundredths limit governs the final addition.

Question 44

A measured product is carried as 0.43821 with a three-figure limit. What last place does it contribute to a following addition?

Accepted Answer

Thousandths

Its reportable form is 0.438. The three retained figures reach the thousandths place; carry the full 0.43821.

Question 45

Report (0.84 + 0.037) × (3.15 − 0.72). Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

2.1

Carry 0.877 and 2.43; their product is 2.13111. The sum’s hundredths limit gives 0.88, two figures. The difference has three figures, so report two.

Question 46

A measured difference is carried as 0.146 with a hundredths reporting limit. What figure count does it contribute to a following division?

Accepted Answer

Two

Its reportable form is 0.15, which has two figures. The subtraction’s place limit does not preserve the original operands’ digit counts.

Question 47

Every calculation in a lab report obeys significant-figure rules. Does that establish that the instrument was correctly calibrated?

Accepted Answer

No

Digit reporting cannot detect a systematic calibration error. Calibration requires independent checks against appropriate references.

Question 48

Report 9.984 ÷ 1.001 + 0.0362. Use introductory significant-figure rules; measured abstract inputs, units omitted.

Accepted Answer

10.010

Carry quotient 9.974025974… and sum 10.010225974…. The quotient’s four-figure form is 9.974, ending at thousandths. Addition keeps that place even after crossing 10, so the final report has five figures.

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Significant Figures Flashcards: Mixed Operations & Rounding