Significant Figures and Rounding Rules Explained With Examples
October 21, 2026
Significant figures, often shortened to sig figs, are the digits in a measurement that carry real information about its precision. Reporting 12.3 cm tells the reader the measurement is good to the nearest tenth of a centimeter. Reporting 12.3000 cm claims precision to the nearest hundred-thousandth. If the true measurement only justified the first claim, the long number is misleading.
Calculators display many digits, but the result can never be more precise than the inputs. Significant-figure rules keep reported answers honest.
Skip the math and get your answer instantly:
Open the Scientific Calculator →Rules for Counting Significant Figures
1. All non-zero digits are significant: 4,827 has four. 2. Zeros between non-zero digits are significant: 5,003 has four. 3. Leading zeros are not significant: 0.0042 has two. 4. Trailing zeros after a decimal point are significant: 2.500 has four. 5. Trailing zeros in a whole number without a decimal point are ambiguous: 1,200 may have two, three, or four. Scientific notation removes the ambiguity: 1.2 × 10³ has two, and 1.200 × 10³ has four.
| Number | Significant figures | Reason |
|---|---|---|
| 4,827 | 4 | All non-zero digits |
| 5,003 | 4 | Zeros between non-zero digits count |
| 0.0042 | 2 | Leading zeros do not count |
| 2.500 | 4 | Trailing zeros after a decimal count |
| 1.2 x 10^3 | 2 | Scientific notation is explicit |
Rounding to a Set Number of Sig Figs
Identify the digit in the last place you want to keep, then look at the next digit. If it is 5 or more, round up; if less than 5, leave it. Round 3.14159 to three sig figs: 3.14. Round 0.0078652 to two sig figs: 0.0079. Round 24,680 to three sig figs: 24,700.
Some fields use banker's rounding (round half to even), where exactly 2.5 rounds to 2 and 3.5 rounds to 4. It reduces systematic upward bias in large sets of numbers and is the default in some software.
Multiplying and Dividing
The result should have the same number of significant figures as the input with the fewest. For a rectangle measured 4.52 m by 2.1 m, the product is 9.492 m², but the width has only two sig figs, so report 9.5 m². For 15.0 ÷ 4 where 4 is a counted number, not a measurement, it has unlimited sig figs, and the answer is 3.75 with three sig figs.
Exact numbers such as counts (12 eggs) and defined conversions (100 cm per meter) do not limit precision.
Adding and Subtracting
For addition and subtraction, keep the number of decimal places of the least precise value, not the number of sig figs. 12.11 + 0.3 + 1.256 = 13.666, which rounds to 13.7 because 0.3 has only one decimal place. Subtracting 15.2 − 14.9 gives 0.3, a single significant figure, so near-equal subtraction loses precision quickly.
This is why small differences between large measurements can be unreliable.
Rounding at the End
Carry extra digits through intermediate steps and round only the final answer. Rounding at each step accumulates error. For example, computing (1/3) × 3 with 0.33 gives 0.99 instead of 1. Calculators keep many digits internally, so use stored values rather than retyping rounded ones.
Money and Everyday Rounding
Financial calculations round to the cent, and rules for rounding half cents vary by jurisdiction and contract. When you compute tax on each line and on the total, results can differ by a cent. Follow the convention required by the invoice or the tax authority.
Frequently Asked Questions
How many significant figures does 0.00450 have?
Three: 4, 5, and the trailing 0 after the decimal point.
Why do significant figures matter?
They communicate the precision of a measurement and prevent overstating accuracy.
How do I round 2.345 to three sig figs?
Look at the next digit, 5, and round up to 2.35 under the usual half-up rule (banker's rounding would give 2.34).
Do exact numbers limit sig figs?
No. Counted values and defined constants are treated as having unlimited sig figs.
Should I round intermediate results?
No. Keep extra digits and round only the final answer.