Count the significant figures in a number, round to a set number of them, or add, subtract, multiply and divide with the sig fig rules, with each rule explained. Runs on your device.
To count significant figures, find the first nonzero digit and count every digit from there to the end, with one exception: zeros at the end of a whole number with no decimal point are not counted. The page opens on 0.004050. The three zeros before the 4 only place the decimal point, so they do not count. The 4, the 0 between 4 and 5, the 5 and the final 0 all count, which gives 4 significant figures. The final zero counts because it comes after a decimal point: it shows the number was measured to the millionths place. The same digits give different answers by how they are written. 1200 has 2, 1200. has 4 and 1.20e3 has 3.
There are three kinds of zero. Leading zeros never count. Zeros between nonzero digits always count, so 305 has 3. Trailing zeros count when the number has a decimal point, so 100 has 1, 100. has 3 and 100.0 has 4. In scientific notation every digit in front of the exponent counts, so 1.20 × 10³ has 3 and 6.022e23 has 4. A value of zero has no digit to start from, and books differ on it; this page counts 1. An exact number, such as 12 eggs or the 100 centimetres in a metre, has no uncertainty and never limits an answer. In the calculate mode, tick the Exact box for such a number.
Rounding keeps the first N digits from the first nonzero digit, then looks at the next one: 5 or more rounds up, 4 or less rounds down. 123.456 to 4 significant figures is 123.5, because the digit after 1234 is 5. To 2 it is 120. The page works on the digits as text, so 1.005 to 3 figures is 1.01 with no floating point error. If a number has fewer digits than you ask for, zeros are added to show the precision: 1.2 to 4 figures is 1.200. A rounded whole number such as 120 hides which zeros count, so the page also shows 1.2 × 10², which states exactly 2.
For addition and subtraction, the answer keeps the decimal places of the least precise number. 12.11 + 18.0 is 30.11 exactly, and 18.0 has one decimal place, so the answer is 30.1. For multiplication and division, the answer keeps as many significant figures as the factor with the fewest. 6.5 × 2.40 is 15.6 exactly. 6.5 has 2 figures and 2.40 has 3, so the answer has 2: 16. The unrounded result is worked out first and rounded once at the end, and the page shows both (a repeating quotient such as 1 ÷ 3 is cut after a few extra digits, not stored as a fraction). The working box states the rule and the numbers. For a chain such as (a + b) × c, do one step at a time and keep the extra digits until the last step.
It does not decide how many figures a measurement deserves, which depends on the instrument. Counting trailing zeros in a whole number follows the usual textbook convention; some teachers treat 1200 as ambiguous, and the notes beside the answer say when that matters. Input can be up to 100 characters with an exponent between −300 and 300. It does one operation at a time, and it rounds halves upward in size, so 2.5 to 1 figure is 3 and −2.5 is −3. Banker rounding is not offered.
Start at the first nonzero digit and count to the end, then take away the zeros at the end of a whole number that has no decimal point. 0.004050 has 4, 1200 has 2, 1200. has 4 and 1.20e3 has 3. Type the number and a table shows which digits count and why.
Only when the number has a decimal point. 100 has 1 significant figure, 100. has 3 and 100.0 has 4. A written 1200 is usually read as 2, and writing 1.200 × 10³ shows 4. This page follows that convention.
Round the answer to the decimal place of the least precise number. 12.11 + 18.0 = 30.11, and 18.0 only goes to tenths, so the answer is 30.1. It is the position of the last digit that matters here, not the number of figures.
Round the answer to the number of significant figures in the factor with the fewest. 6.5 × 2.40 = 15.6, and 6.5 has 2 figures, so the answer is 16. Use the Exact boxes for counted or defined numbers, which do not limit the answer.
Choose Round to sig figs and set the figures to 3. 0.0012349 becomes 0.00123 and 999.5 becomes 1000, written 1.00 × 10³. The page shows the digits it kept, the digit it looked at to round up or down, and the result in scientific notation.
No. The numbers are processed in your browser and are not uploaded. They are not stored on your device either, and reloading the page puts the 0.004050 example back.