# Significant Figures Calculator

## Calculator Use

This calculator will round a number to a specified number of significant figures. Only significant digits will be displayed in the answer. When an integer contains more digits than are significant, the last significant digit will be underlined.

## Significant Figures Rules

Significant figures are the digits of a number that are meaningful in terms of precision, or in other words, the digits that are giving us meaningful information about how precise a calculation or measurement is. Here are some examples of numbers and their associated significant figures.

Significant Figures?

are Significant?

__0__0

### Significant Figures:

- Any non-zero digit
- Zeros between non-zero digits (
**Example:**3003) - Trailing zeros when a decimal point is present (
**Example**: 274.333300 or 6750.)

### Not Significant Figures:

- Leading zeros (
**Example:**0.009 or 022) - Trailing zeros when no decimal point is present (unless indicated otherwise with an underline or bar over the digit)

For more information on why we consider a digit a significant or not, see the Khan Academy's module on significant figures.

## Rounding Rules

We can round numbers to a specified number of significant figures. This becomes necessary when we perform a mathematical operation involving numbers with multiple levels of precision (i.e., differing numbers of significant figures). For example, if we were adding two measurements with different numbers of significant digits, the result can only be as precise as the measurement with the fewest significant digits.

**Example: **Say we measured the lengths of two trains - one train was measured using distance markers, and came out to a length of 1.1 miles, the second train was measured using a more accurate laser with a length of 1.283 miles. If we added the lengths as is (1.1 mi + 1.213 mi), we'd come to an answer of 2.313 miles. This would not be correct however, since the first train was only measured within a tenth of a mile, and the second was much more accurately measured to a thousandth of a mile. We would need to round the answer to the match the length with the lowest amount of precision, or significant digits - in this case, 2.313 mi rounded to two significant figures would be rounded to 2.3 mi.

When rounding to a given number of significant figures, the standard rules of rounding typically apply, except that non-significant figures to the left of the decimal are replaced with zeros.

Here is an example: **305.459** is shown rounded to between 0 and 6 significant figures, and for comparison, the same number is rounded to between 0 and 6 decimal places:

sf or dp?

Significant Figures (sf)

Decimal Places (dp)

## References

- Khan, Salman "Significant Figures,"
*The Khan Academy*. - Weisstein, Eric W. "Significant Digits,"
*MathWorld*--A Wolfram Web Resource.

**Cite this content, page or calculator as:**

Furey, Edward "Significant Figures Calculator"; from *http://www.calculatorsoup.com* - Online Calculator Resource.