Practice Significant Figures in Math

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

Quick Recap

Significant figures are the meaningful digits in a measured quantity, reflecting its precision.

Think of them as the digits you can trust from a measuring tool.

Showing a random 20 of 50 problems.

Example 1

medium
How many significant figures does 1.020ร—1031.020 \times 10^{3} have?

Example 2

medium
A student rounds 3.653.65 to two sig figs by standard 'round half up' and writes 3.73.7. Is that correct?

Example 3

medium
Compute 3.6ร—2.413.6 \times 2.41 and report with the correct number of significant figures.

Example 4

easy
Round 0.046810.04681 to two significant figures.

Example 5

easy
How many significant figures does 452452 have?

Example 6

hard
A rectangle has length 12.4612.46 cm (4 s.f.) and width 3.23.2 cm (2 s.f.). Compute the perimeter and the area with correct rules.

Example 7

easy
Round 7.8467.846 to two significant figures.

Example 8

medium
Express 345,000345{,}000 with exactly 22 significant figures in scientific notation.

Example 9

medium
Round 0.00487290.0048729 to three significant figures.

Example 10

challenge
Why is rounding intermediate steps to fewer significant figures considered bad practice? Illustrate with (1.236+2.341)ร—3.0(1.236 + 2.341) \times 3.0 computed two ways.

Example 11

easy
How many significant figures does 0.00009000.0000900 have?

Example 12

medium
Compute 6.421.2\frac{6.42}{1.2} and report with the correct significant figures.

Example 13

easy
How many significant figures does 3.143.14 have?

Example 14

easy
Round 3.8463.846 to two significant figures.

Example 15

challenge
Evaluate (3.0ร—102)+(4.50ร—103)(3.0 \times 10^2) + (4.50 \times 10^3) and report with correct significant figures.

Example 16

easy
Count the significant figures in each number: (a) 0.004200.00420, (b) 3,0503{,}050, (c) 7.300ร—1047.300 \times 10^4.

Example 17

challenge
A density is found by ฯ=m/V\rho = m/V with m=12.34m = 12.34 g (4 s.f.) and V=5.0V = 5.0 mL (2 s.f.). Report ฯ\rho with correct sig figs.

Example 18

easy
How many significant figures does 1,0081{,}008 have?

Example 19

challenge
Why does 0.005000.00500 have three significant figures while 500500 (no decimal) has one? Round 0.005000.00500 to one sig fig.

Example 20

medium
Round 25โ€‰84725\,847 to two significant figures.