# Significant Figures Calculator

### Calculate significant figures instantly

## What are significant figures?

Significant digits, or sig figs for short, are the significant digits in a number. Leading zeroes and trailing zeroes may be removed without affecting the accuracy of the number (004 is equivalent to 4). Significant figures must be identified in order to preserve the accuracy of a number when rounding it up or down. One or more significant figures are changed when you round a number up or down.

## Sig figs calculator operators

The following operators and functions can be used with this calculator: Addition ( + ), subtraction ( - ), division ( / or ÷ ) and multiplication ( * or x ). Plus exponent ( ^ ) Parentheses ({ }) Functions: log, ln A counter is also provided that keeps track of the number of significant digits for each calculation.

## How many significant figures are there in...?

Here are some examples of significant figure calculations:

- 7 has 1 significant figure (7).
- 73 has 2 significant figures (7 and 3).
- 100 has 1 significant figure (1).
- 673 has 3 significant figures (6, 7 and 3).
- 673.52 has 5 significant figures (6, 3, 7, 5 and 2).
- 0.0637 has 3 significant figures (6, 3 and 7).
- 30.00 has 4 significant figures (3, 0, 0 and 0) and 2 decimals.
- 0.0025 has 2 significant figures (2 and 5) and 4 decimals.

## How to count significant figures

Here are the criteria you should know for determining significant figures.

**All of the following are significant figures:**

- Every non-zero digit is always significant.
- When the digits in a phone number are put together, for example, 5-0 is significant because it's between other numbers such as 205 or 3.604 (because clearly, 25 isn't the same as 205).
- If a decimal point is present, any trailing zeroes are significant figures (e.g., 90.75). These trailing zeroes may appear to be irrelevant at first sight, but they do confirm the precision of the number. 90.75 could very well be 90.7511 rounded down to two digits after rounding up to four places. As a result, 90.7500 confirms that it is completely precise to four decimal places

**And these are not significant figures…**

- Leading zeroes before a non-zero digit are not significant figures, as the preceding example illustrates (00200 is the same as 200 and 007 is the same as 7, so leading 0s are not significant). Leading zeros can be confusing because they are not significant figures even if they come after a decimal place. The problem with the finest zeroes is that they may appear to be important because 0.01kg of grapes isn't the same as 1kg of grapes. The leading zeroes, on the other hand, might seem significant since 0.01 kg can also be represented as 10 g. It's the same value (10g). As a result, leading zeroes aren't considered to be crucial figures; it's just the 1 part that matters. If the zero is between two significant figures (e.g. 2.303), it is significant, in accordance with rule (2) stated above.
- When there are no decimal points, trailing zeroes are not significant. Any trailing zeroes will be considered significant figures if there is a decimal point, as per rule (3) above.

## Calculator Usage

Count the number of significant figures in a number, and identify which digits are significant. This calculator may be used for significant figure practice: Test your skill at finding out how many significant figures are in a number.

Enter whole numbers, real numbers, scientific notation (e), or e notation. 3500, 35.0056, 3.5 x 10^3, and 3.5e3 are some of the examples given.

## Doing Math With Significant Figures

If you're entering a constant or exact value, as you might encounter in a formula, make sure to include the correct number of significant figures.

Consider the formula for circle diameter, d = 2r, where d is twice the radius length. To determine the diameter of a circle, multiply by 2 to get 4.70: if you measure a radius of 2.35, divide by 2 to obtain the diameter of the circle: n2 * 2.35 = 4.70n

If you use this calculator for the calculation and only type in "2" for the radius value, the calculator will interpret the number as a single significant figure. Your final result will be rounded down to 4.70 instead of 2. As a result, your diameter calculation d=2r was incorrect.

Constants or precise values can be thought of as having an infinite number of significant figures, or at the very least a comparable number of significant figures to the most imprecise figure in your calculation. In this case, you should input 2.00 for the constant value so that it has the same amount of significant digits as the radius entry. The calculated result is 4.70, which has three significant figures.