Practice Precision in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The degree of exactness in a measurement or calculation, reflected in the number of significant digits reported.

How many decimal places matter? Measuring in inches vs. millimeters.

Showing a random 20 of 50 problems.

Example 1

medium
Express 123,000123{,}000 with 33 significant figures using scientific notation.

Example 2

medium
Multiply 3.43.4 cm ร—\times 2.152.15 cm, applying the significant figures rule for multiplication.

Example 3

medium
A board is measured as 1.501.50 m and another as 1.51.5 m. How do their precisions differ?

Example 4

medium
A student computes ฯ€ร—r2\pi \times r^2 with r=2.5r = 2.5 cm and reports 19.6349541โ€ฆ19.6349541\ldots cm2^2. What is the appropriate result respecting the precision of rr?

Example 5

easy
Round 0.007980.00798 to 22 significant figures.

Example 6

medium
Three measurements: 4.24.2, 4.184.18, 4.2054.205. Identify the precision (decimal places) of each and the precision of their average if reported correctly.

Example 7

medium
Multiply 2.1ร—3.22.1 \times 3.2 and report with correct significant figures.

Example 8

medium
Round 3.141593.14159 to (a) 33 sig figs, (b) 55 sig figs.

Example 9

easy
Round 7.867.86 to 22 significant figures.

Example 10

medium
A digital thermometer reads 36.7โˆ˜36.7^\circC. What is the absolute uncertainty implied by the display?

Example 11

challenge
Explain why writing 2.1ร—3.2=6.72002.1 \times 3.2 = 6.7200 is misleading even though the arithmetic gives 6.726.72.

Example 12

hard
Distinguish precision and accuracy with an example: a target shooter places 55 shots in a tight cluster 1010 cm to the left of the bullseye.

Example 13

easy
How many significant figures does 0.00240.0024 have?

Example 14

challenge
Two students measure the same rod: A reports 25.025.0 cm, B reports 25.0025.00 cm. If only a mm ruler was used, who has reported an honest precision?

Example 15

easy
How many significant figures does 0.00500.0050 have?

Example 16

easy
Which measurement is more precise: 77 m, 7.07.0 m, or 7.007.00 m? How many significant figures does each have?

Example 17

medium
Round 0.049850.04985 to 22 significant figures.

Example 18

hard
Compute (2.34ร—4.5)+1.245(2.34 \times 4.5) + 1.245 with correct sig fig and decimal-place rules at each step.

Example 19

easy
Which measurement is more precise: 55 cm or 5.05.0 cm?

Example 20

hard
A measurement is reported as 6.20ยฑ0.056.20 \pm 0.05 cm. What is the percent uncertainty?
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