# Calculate and count Sig Figs (Significant Figures)!

## Output:

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## How to use the Sig Fig Calculator and Counter?

Time needed: 1 minute.

1. Enter the Number

Write or paste a number or an expression into the first field.
Optionally, specify the number of Sig Fig to round up to.

2. Press the Calculate button

Press the Calculate button below the number field.

3. Review the Output

The results will appear in the Output field.

4. Copy or Save the result

Optionally, you can Copy the output to clipboard, or Save it as a file on your device.

## What are Significant Figures? Sig Figs definition

Significant Figures (often shorted as Sig Figs, and also known as Significant Digits) are defined as the digits in a number that contribute to the degree of accuracy of the expression of number.

Significant Figures are often used to express the precision of measured values: Sig Figs represent the digits in the value which can be reliably measured by the measurement tool itself.

## What are the Significant Figures rules?

• All non-zero digits are significant:
• 1.234 g has 4 significant figures,
• 1.2 g has 2 significant figures.
• Zeros between two significant digits are significant:
• 1005 km has 4 significant figures,
• 4.02 L has 3 significant figures.
• Leading zeros are not significant:
• 0.001 g has only 1 significant figure,
• 0.013 g has 2 significant figures.
• Trailing zeros are not significant when numbers don’t have a decimal point, or when they are mere placeholders:
• 540 m has 2 significant figures,
• 540.0 m has 4 significant figures.
• Exact numbers have an infinite number of significant digits.

## How to count the Significant Figures of a number?

Count all the digits that are significant in a number. They include:

• Non-zero digits,
• Zeros between non-zero digits,
• Trailing zeros only when there is a decimal point.

## How to identify Not Sig Figs?

The following digits are not significant figures:

• Trailing zeros when they are place holders: for example, the trailing zeros in 1500 mg are not significant if they are just placeholders for ones and tens places as the measurement resolution is 100 mg.
• Spurious digits, that can be introduced by calculations resulting in a number with a greater precision than the precision of the data used in the calculations.
• In scientific notation, all digits before the multiplication sign are significant.

## How do you round off to an arbitrary number of Sig Figs?

To round a number to the desired amount of significant figures, do the following:

• Drop all the remaining digits after the first N significant figures (where N is the number of Sig Figs you want to round off a number to)
• Round the number down to the nearest integer if the leftmost dropped digit is ≤ than 4, round the number up if the leftmost dropped digit is ≥ 6.
• If the digit to be dropped is 5 and is followed only by zeroes, round up to the even digit.
• Add a zero for each dropped number that is not a decimal.

Example: round 718.49 to 2 significant figures.

Take the first 2 significant digits, 7 and 1.

The leftmost dropped digit is 8, so round up to 72 and then add a 0 to the result, which is 720.

## Significant figures in operations

When carrying out mathematical calculations, the accuracy of the result is limited by the least accurate measurement involved in the calculation.

For addition and subtraction operations, the result is rounded off to reflect the precision of the component with the least number of decimals.

For example: 114.3 + 2.151 = 116.451, which should be rounded to 116.5.

### Multiplication and division

For multiplication and division, the result is rounded off to have the same number of significant figures of the component with the least number of significant figures.

For example: 2.51 x 4.395 = 11.03145, which should be rounded to 11.0 (3 significant figures).

### Mixed calculations

When doing mixed calculations (i.e. addition/subtraction and multiplication/division) – you need to note the number of significant figures for each step of the calculation.

For example, for the expression 5.4 + 9.815 * 2.01 the first step would result in 5.4 + 19.72815. This intermediate result should not be rounded. But the final result, 25.12815 should be rounded to 25.1 to reflect the number of sig figs of the intermediate step.