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: Only report as many digits as your least-precise measurement justifies—a result cannot be more precise than its inputs.

Common stuck point: Leading zeros are never significant; trailing zeros after a decimal are significant; trailing zeros in whole numbers are ambiguous.

Sense of Study hint: Mark the first and last trustworthy digit, then count only digits in between.

Worked Examples

Example 1

easy
Count the significant figures in each number: (a) 0.00420, (b) 3{,}050, (c) 7.300 \times 10^4.

Solution

  1. 1
    (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.
  2. 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. 3
    (c) 7.300 \times 10^4: scientific notation makes it clear. Digits 7, 3, 0, 0 are all significant. 4 significant figures.

Answer

(a) 3 sig figs; (b) 3 or 4 sig figs (ambiguous); (c) 4 sig figs.
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.

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 25.00 mL of solution using a burette and 0.5 mL using a dropper. She adds them. What is the total volume with correct significant figures?
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Background Knowledge

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

roundingprecisionscientific notation