Significant Figures Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Significant Figures.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept 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.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Significant figures count which digits in a measurement actually carry real information about its precision.

Common stuck point: The procedure for significant figures is the easy part; the trap is counting leading zeros as significant. Asking "Does this digit carry real information from the measurement, or is it just placing the decimal point or padding the calculator?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does this digit carry real information from the measurement, or is it just placing the decimal point or padding the calculator?

Worked Examples

Example 1

easy

Count the significant figures in each number: (a)

0.00420

, (b)

3{,}050

, (c)

7.300 \times 10^4

Answer

(a)

3

sig figs; (b)

3

4

sig figs (ambiguous); (c)

4

sig figs.

First step

(a)

0.00420

: leading zeros are not significant. The digits

4

2

0

are significant (trailing zero after a non-zero digit past the decimal point counts).

3

significant figures.

Full solution

2
(b) $3{,}050$ : without a decimal point, the trailing zero is ambiguous. The definite significant figures are $3$ , $0$ (the middle zero between non-zeros counts), $5$ — at least $3$ sig figs; the trailing zero may or may not be significant.
3
(c) $7.300 \times 10^4$ : scientific notation makes it clear. Digits $7$ , $3$ , $0$ , $0$ are all significant. $4$ significant figures.

Rules: leading zeros are never significant; captive zeros (between non-zeros) are always significant; trailing zeros after the decimal point are significant; trailing zeros before the decimal without a decimal point are ambiguous. Scientific notation removes all ambiguity.

Example 2

medium

A rectangle measures

4.5

cm by

3.25

cm. Calculate the area to the correct number of significant figures.

Example 3

medium

A car travels

124.6

km in

2.0

hours. Report its average speed with correct significant figures.

Example 4

hard

A rectangle has length

12.46

cm (4 s.f.) and width

3.2

cm (2 s.f.). Compute the perimeter and the area with correct rules.

Example 5

challenge

Why is rounding intermediate steps to fewer significant figures considered bad practice? Illustrate with

(1.236 + 2.341) \times 3.0

computed two ways.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Round each to

3

significant figures: (a)

0.0046872

, (b)

12{,}350

, (c)

999.6

Example 2

medium

A chemist measures

easy

How many significant figures does

0.030

have?

Example 9

easy

How many significant figures are in

to two significant figures.

Example 20

challenge

A rectangle measures

2.5

cm by

1.20

cm. Report its area with the correct significant figures.

Example 21

challenge

Evaluate

(3.0 \times 10^2) + (4.50 \times 10^3)

and report with correct significant figures.

Example 22

challenge

Why does

0.00500

have three significant figures while

medium

Express

345{,}000

with exactly

2

significant figures in scientific notation.

Example 35

medium

A student rounds

3.65

to two sig figs by standard 'round half up' and writes

3.7

. Is that correct?

Example 36

hard

Compute

(1.20\times 10^{3})(4.0\times 10^{-2})

and report with correct sig figs.

Example 37

hard

A measurement is

24.05

cm. A rod is built up by laying

5

such measurements end to end. Report the total length with correct precision.

Example 38

hard

A circle has measured radius

r=3.50

cm. Compute its circumference with correct sig figs using

\pi \approx 3.14159

Example 39

challenge

A density is found by

\rho = m/V

with

m = 12.34

g (4 s.f.) and

V = 5.0

mL (2 s.f.). Report

\rho

with correct sig figs.

← Back to Significant Figures Practice Mode

Related Concepts

Rounding Precision Scientific Notation

Background Knowledge

These ideas may be useful before you work through the harder examples.

roundingprecisionscientific notation