Does 1200 have two significant figures or four?

By convention, two. Without a decimal point there is no way to know whether the zeros were measured, so they are treated as placeholders. Write 1.200 times ten cubed if you mean four.

How many figures should a result carry?

For multiplication and division, as many as the least precise input. For addition and subtraction, as many decimal places as the least precise input. Carrying more implies precision that was never measured.

Math & Statisticsnotation

Significant Figures Calculator

How many significant figures a number carries, and rounding to a chosen count. Trailing zeros are the whole difficulty: 1200 has two, and 1200.0 has five.

Also called: sig figs calculator, significant digits.

Significant figures in what you entered

0.00340 has 3 significant figures. Rounded to 3 of them it is 0. The decimal point makes every trailing zero count.

Rounded to your figure count

In scientific notation, where the count is unambiguous

3.4 x 10^-3

Decimal places

Why the count is what it is

The decimal point makes every trailing zero count.

How this is calculated

Method and background

How this is calculated

Counting starts at the first non-zero digit, so leading zeros are placeholders and never count. Trailing zeros are ambiguous without a decimal point: writing 1200 gives no way to tell whether the zeros were measured or rounded, so convention says they do not count. Adding a decimal point removes the doubt, and scientific notation removes it entirely, which is why measurements are recorded that way.

leading zeros never count; trailing zeros count only when a decimal point is present

n: The number as written

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

leading zeros never count

Number as written: 0.00340
Round to how many significant figures: 3

Significant figures in what you entered3

Three, four and zero; the leading zeros are placeholders

Open this example

a decimal point makes them count

Number as written: 1200.0
Round to how many significant figures: 5

Significant figures in what you entered5

The same digits, a different claim about precision

Open this example

trailing zeros without a point do not count

Number as written: 1200
Round to how many significant figures: 2

Significant figures in what you entered2

boundary: the ambiguity the convention exists to resolve

Open this example

Method and limits

What it assumes

The number is entered as written, since the count depends on the writing rather than the value.

What it deliberately does not model

A count in the presence of an overbar or an explicit uncertainty is a notation this does not parse.

Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator

Frequently asked questions

Does 1200 have two significant figures or four?: By convention, two. Without a decimal point there is no way to know whether the zeros were measured, so they are treated as placeholders. Write 1.200 times ten cubed if you mean four.
How many figures should a result carry?: For multiplication and division, as many as the least precise input. For addition and subtraction, as many decimal places as the least precise input. Carrying more implies precision that was never measured.