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Significant Figures Calculator

Count the significant figures in a number exactly as written, and round it to any number of significant figures.

Level: Grades 9–10

Printable worksheet

Significant Figures Calculator

Inputs

Type it exactly as written, for example 0.00450, 1200, 1200. or 4.50e-3. Zeros at the end matter.

Optional. Leave blank to only count.

Result

Significant figures

3

0.00450 has 3 significant figures.

If the trailing zeros were measured
Not applicable: no ambiguous zeros
Significant digits
450
Decimal places as written
5
In scientific notation
4.50 × 10^-3
Rounded to 2 significant figures
0.0045
Rounded, in scientific notation
4.5 × 10^-3

See the step-by-step solution ↓

Step-by-step solution

  1. Start from the digits exactly as you typed them. Minus signs and commas are not digits

    0.00450

  2. Zeros in front only show where the decimal point is, so these 3 zeros are not significant

    not significant: 0 0 0

  3. Zeros at the end count when there is a decimal point. They show the value was measured to that place

    significant: 0

  4. Count the digits that are significant

    significant digits 4 5 0=3

  5. To keep 2 significant figures, round at the place of digit number 2. That place is 10^-4, and a 5 rounds up

    unit=10−4

  6. Here is the rounded value, keeping any zeros at the end that now count

    0.0045 = 4.5 × 10^-3

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how many significant figures a number has, and round it to as many as you need. Significant figures (sig figs) are the digits that show how precisely something was measured. A length written as 2.50 m is measured to the nearest centimetre. Written as 2.5 m, it's only measured to the nearest tenth of a metre. The two are the same number, but they say different things about the measurement. Science and engineering use sig figs so a result never claims more precision than the measurements behind it.

Type your number exactly as it was written, with any zeros at the end and any decimal point. Those details carry the precision. The calculator walks through the counting rules one at a time and explains each one. It shows the significant digits and the number in scientific notation (a form like 4.50 × 10^-3). It also flags numbers like 1200, where the zeros at the end could go either way. If you choose how many sig figs to keep, it rounds the number too. It does the math on the exact digits you typed, so tricky cases like 1.005 → 1.01 come out right.

Where it's used

Why this math matters outside the classroom:

  • Lab reports. A student who measures 12.0 mL and 3.25 mL reports their sum as 15.3 mL, matching the less precise reading.
  • Density results. Dividing 25.4 g by 3.1 cm³ gives about 8.19355, which is reported as 8.2 g/cm³ to two significant figures.
  • Engineering drawings. A machinist reads a dimension of 2.500 in as four significant figures, meaning it must be made to the thousandth.
  • Counting zeros. Students learn that 0.00450 has three significant figures, because leading zeros don't count but the trailing zero does.
  • Crowd estimates. A reported crowd of 30,000 has one or two significant figures, not five, because it is an estimate.

Grade level and standards: Grades 9–10; Common Core State Standards for Mathematics HSN.Q.A.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Type the number exactly as written, for example 0.00450, 1200, 1200. or 4.50e-3. Scientific notation such as 4.50 × 10^-3 works too.
  2. If you want to round, enter how many significant figures to keep. Leave it blank if you only want to count.
  3. Read the count at the top. Below it are the significant digits, the scientific notation and any rounded result.

What the inputs mean

Number
The calculator reads your number as text, digit by digit, so 2.50 and 2.5 are treated differently, as they should be. Commas between thousands are fine. It won't accept exactly zero, because the counting rules depend on digits that aren't zero.
Round to (significant figures)
A 5 rounds up (away from zero), as most science classes teach. If you ask for more figures than the number has, zeros are added at the end. Only do that if the measurement really was that precise.

Formula and method

1. Nonzero digits are always significant.
2. Zeros between nonzero digits are significant.
3. Leading zeros are never significant.
4. Trailing zeros are significant when the number has a decimal point.
5. Trailing zeros in a whole number without a decimal point are ambiguous.
rounding unit = 10^(L − N + 1), where L is the place of the leading digit

Leading zeros are the zeros in front, as in 0.00450. They only show where the decimal point goes. Write the same value as 4.50 × 10^-3 and they disappear, so they can't carry precision. Zeros between other digits, as in 1002, were measured, so they always count.

Trailing zeros are the zeros at the end. After a decimal point, as in 2.50, they're there on purpose. Nobody writes them unless the measurement reached that place, so they count. In a whole number such as 1200, they might be measured or might just be placeholders. This calculator follows the common habit of not counting them. It also shows what the count would be if they were measured. Writing 1200. (with a decimal point at the end) or 1.200 × 10^3 clears up the doubt.

To round to N significant figures (N is how many you want to keep), first find the place of the leading digit. That place is a power of ten, called L. For 0.00450, the 4 sits in the thousandths place, so L is −3. Then round to whole units of 10^(L − N + 1). The rounding works on the exact digits you typed, not a computer's binary estimate, so numbers that sit exactly halfway round correctly.

Worked example

Count the significant figures in 0.00450, then round to 2 significant figures.

  1. The zeros in front, 0.00, only show where the decimal point is, so they are not significant.
  2. The digits 4 and 5 are not zero, so they are significant.
  3. The last 0 comes after a decimal point, so it is significant.
  4. That gives 3 significant figures: 4, 5 and 0, or 4.50 × 10^-3.
  5. To keep 2 significant figures, round to units of 10^-4: 0.00450 becomes 0.0045.

Result: 0.00450 has 3 significant figures. Rounded to 2 significant figures, it is 0.0045 (4.5 × 10^-3).

Understanding the result

More significant figures means a more precise value. When you multiply or divide, keep as many sig figs as the least precise number you started with.

When you add or subtract, the rule is about decimal places instead. Keep as many decimal places as the number with the fewest. That's why the calculator shows decimal places too.

If a whole number's count is marked ambiguous, think about how the value was measured. A population of 1200 counted exactly has 4 significant figures. A crowd estimate of 1200 may have only 2.

Assumptions and limitations

  • You typed exactly the digits that were measured or reported.
  • Zeros at the end of a whole number aren't counted, unless the number has a decimal point or is in scientific notation.
  • Exact numbers have unlimited significant figures. That includes counted items and defined amounts, like 100 cm in a metre. The calculator can't tell these apart from measured values.
  • Zero itself can't be counted with these rules.
  • Rounding goes up to 30 significant figures.

Frequently asked questions

How many significant figures does 100 have?

By the usual convention, 1, because the zeros at the end might only be placeholders. If they were measured, write 100. or 1.00 × 10^2. Both of those have 3.

Are significant figures the same as decimal places?

No. Decimal places count the digits after the decimal point. Significant figures count the meaningful digits, wherever they are. So 0.0045 has 4 decimal places but only 2 significant figures. And 4,500.0 has 1 decimal place but 5 significant figures.

Why does scientific notation make sig figs clear?

In scientific notation, every digit in front of the power of ten is significant. Leading zeros and placeholder zeros disappear into the exponent (the small number after the 10). So 1.20 × 10^3 has 3 significant figures, with no doubt about it.

How should I round when the next digit is exactly 5?

This calculator rounds a 5 up (away from zero), the rule most classes teach. Some labs and standards round a 5 to the nearest even digit instead. That keeps results from drifting upward over many roundings. The rounding calculator offers both methods.

How this calculator is checked

Method: Standard significant-figure counting rules for measured values; exact decimal rounding to a power-of-ten unit (half up). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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