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IntoChemistry · General Chemistry

Significant Figures: Rules & Practice

Learn which digits count, how to round calculated results, and how to avoid the mistakes most students make.

◎ Clear explanations◉ Worked examples▤ Practice problems⬇ Free resources

What are significant figures?

Significant figures communicate the precision of a reported measurement. For example, 12.30 cm has four significant figures: the last zero indicates the value was measured to the hundredths place.

Illustrated Significant Figures: Rules & Practice study overview
IntoChemistry visual guide. Follow the worked examples below for the complete reasoning.

A five-rule method

  1. All nonzero digits count. 357 has three significant figures.
  2. Zeros between nonzero digits count. 1002 has four.
  3. Leading zeros do not count. 0.0025 has two.
  4. Trailing zeros in decimal measurements count. 2.500 has four.
  5. Whole-number trailing zeros without a decimal point can be ambiguous. Use scientific notation to show precision: 1 × 10³ versus 1.00 × 10³.

See the counting rules

Visual guide to significant figures in numbers with leading, interior and trailing zeros.
Visual guide to significant figures in numbers with leading, interior and trailing zeros.

Worked examples

Worked example

How many significant figures are in 0.00450?

  1. Ignore the zeros before the 4: they only position the decimal point.
  2. Count 4, 5, and the final zero because it follows a decimal-place measurement.

Answer: 3 significant figures.

Worked example

Multiplication and division: 3.20 × 4.5

  1. Calculate the unrounded value: 3.20 × 4.5 = 14.4.
  2. The inputs have three and two significant figures, so report two.

Answer: 14 (two significant figures).

Worked example

Addition: 12.3 + 0.45 + 7.891

  1. Add without early rounding: 12.3 + 0.45 + 7.891 = 20.641.
  2. The least precise term is 12.3 (tenths place). Round to the tenths place.

Answer: 20.6.

Common mistakes

  • Counting leading zeros as significant digits.
  • Using the multiplication rule when adding; addition and subtraction use decimal places.
  • Rounding intermediate values before the calculation is finished.
  • Assuming 1500 has an unambiguous number of significant figures without context.

Quick self-check

How many significant figures are in 7.0200?

Five. The interior zero and both final decimal zeros count.

Interactive Significant Figures: Rules & Practice Practice

Apply what you have learned using immediate feedback.

Practice tool

Significant Figures Trainer

Count the significant figures in the displayed measurement. Use the hint after attempting a question.

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