Significant Figures Calculator

Count significant figures, round them, and apply the rules for multiply, divide, add, and subtract.

Task *

Measurement *

Smart Tips

• Nonzero digits count. Zeros between them count. Leading zeros do not.

• Trailing zeros left of the decimal point do not count on this page, including a number written 100.

• Multiply and divide keep the fewest significant figures. Add and subtract keep the fewest decimal places.

• A lone 5 rounds to the even digit. A 5 followed by a nonzero digit rounds away from zero. Place-value rounding is a separate tool.

The Formula

× and ÷ keep the fewest significant figures + and − keep the fewest decimal places

count Figures in one number
Captive zeros count. Leading zeros do not.

round Keep n figures
A lone 5 rounds to the even digit

× ÷ Product or quotient
Fewest significant figures in the inputs

+ − Sum or difference
Fewest decimal places in the inputs

Enter the measurements as text so trailing zeros survive. A number field would turn 1.00 into 1.

Key Insights

Written digits matter

100 has one significant figure here. 1.00 has three. The decimal point is what makes those trailing zeros count.

Two different rules

Multiplication and division look at significant figures. Addition and subtraction look at decimal places.

Half to even

OpenStax rounds an exact 5, with only zeros after it, to the even retained digit. That is not the school round-half-up rule.

A separate rounding page

Round-half-up to a chosen place, with the deciding digit, is the rounding calculator.

Frequently Asked Questions

Nonzero digits count. Zeros between nonzero digits count. Leading zeros, as in 0.00450, do not. Trailing zeros after a decimal point do count, so 0.00450 has three significant figures.

No. Trailing zeros left of the decimal point are not counted, so 100 has one significant figure. 1.00 has three because those zeros follow a decimal point.

A product or quotient keeps as many significant figures as the less precise input. A sum or difference keeps as many decimal places as the input with the fewest decimal places.

An exact 5 followed only by zeros rounds to the even retained digit. If the dropped digit is greater than 5, or a 5 is followed by a nonzero digit, the result rounds away from zero. Rounding half up to a place value is a different calculator.

A numeric field would drop the trailing zeros in 1.00. Those zeros are part of the measurement, so the page keeps the text you typed.

Counting, the trailing-zero rule, half-to-even rounding, and the rules for multiplication, division, addition, and subtraction follow OpenStax Chemistry 2e, section 1.5, Measurement Uncertainty, Accuracy, and Precision.

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Result

Enter values to calculate

Detail

Rule

Note:Trailing zeros left of the decimal point are not significant. A lone 5 rounds to the even digit, which is the chemistry rule, not round-half-up. Place-value rounding is a separate calculator.