# Significant Figures Calculator – Sig Fig

Created by Daniel Trojanowski and Steven Wooding
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Sep 05, 2024

Use the significant figures calculator to perform arithmetical operations (addition, subtraction, multiplication, division) and get the results rounded to the correct number of significant figures. You can also use this tool as a significant figure counter. Just enter the number, and our sig fig counter will give the number of significant figures in it as well as highlight the least significant digit.

Continue reading to learn what significant figures are. We will also review the common rules of significant figure operations and see how to use the sig fig calculator.

Prefer watching over reading? Learn all you need in 90 seconds with this video we made for you:

## How to use this significant figures calculator

Let us guide you on how to put this calculator to the best use:

1. Enter a number (whole number, real number, or scientific notation). To perform arithmetical operations, enter the expression, for example, 3.14 / 7.58 - 3.15.

2. The significant figures calculator will instantly summarize the results, including the number in decimal notation and the number of significant figures in the number (or expression). It will also underline the least significant digit.

3. If your input involves arithmetical operation, the sig fig calculator will also provide a step-by-step solution.

4. You can choose to round off your results to the desired precision by selecting the "Round to sig fig" option.

5. To use this tool as a sig fig counter, enter the number. You will get the number of significant figures in it.

🔎 The default rounding method is half up, but you can choose a different method if you'd like. To do this, click on the Advanced mode, which will open a new field, "rounding mode," with different options for you to choose from.

For example, consider the number 24.0725. When we enter 24.0725, the significant figures calculator tells us that the number has 6 significant figures and the least significant digit is 5. Additionally, it shows us the decimal notation, the scientific notation, 2.40725 × 101, and the E-notation, 2.40725e+1.

Suppose we want only 3 significant figures for this number. When we input 3 in the round to sig-fig field, the decimal notation 24.1 is immediately available in the results section.

## What are significant figures?

Significant figures are all the digits that indicate the precision of a measurement.

Every measurement involves some degree of uncertainty due to the limitations in the precision of the measuring tool. For example, a standard ruler can only measure to the nearest millimeter. So, if we use it to measure the length of a rod, we can get a value to the nearest of 1/10th of a centimeter. This means we can measure it as, say, 12.5 cm, but we can't measure it to a higher precision, i.e., 12.51 cm. Hence, in this specific example, there are three significant figures in the measured value of 12.5 cm.

It is also highly probable that while measuring this rod, we realized that the length lies somewhere between 12.5 cm and 12.6 cm. Then, we must estimate the length as either 12.5 cm or 12.6 cm; hence, the last digit in this measurement is the first uncertain digit or the least significant digit.

To prevent repeating figures that aren't significant, numbers are often rounded. One must be careful not to lose precision when rounding. Many times the goal of rounding numbers is just to simplify them. Use the rounding calculator to assist with such problems.

In the next section, we will see how to count the significant figures in a measurement.

## What are the significant figures rules?

To determine what numbers are significant and which aren't, use the following rules:

1. The zero to the left of a decimal value less than 1 is not significant.

2. All trailing zeros that are placeholders are not significant.

3. Zeros between non-zero numbers are significant.

4. All non-zero numbers are significant.

5. If a number has more numbers than the desired number of significant digits, the number is rounded. For example, 432,500 is 433,000 to 3 significant digits (using half up (regular) rounding).

6. Zeros at the end of numbers that are not significant but are not removed, as removing them would affect the value of the number. In the above example, we cannot remove 000 in 433,000 unless changing the number into scientific notation.

You can use these common rules to know how to count sig figs.

## More examples of how to use the sig fig calculator

Our significant figures calculator works in two modes – it performs arithmetic operations on multiple numbers (for example, 4.18 / 2.33) or simply rounds a number to your desired number of sig figs.

Following the rules noted above, we can calculate sig figs by hand or by using the significant figures counter. Suppose we have the number 0.004562 and want 2 significant figures. The trailing zeros are placeholders, so we do not count them. Next, we round 4562 to 2 digits, leaving us with 0.0046.

Now we'll consider an example that is not a decimal. Suppose we want 3,453,528 to 4 significant figures. We simply round the entire number to the nearest thousand, giving us 3,454,000.

What if a number is in scientific notation? In such cases, the same rules apply. To enter scientific notation into the sig fig calculator, use E notation, which replaces × 10 with either a lower or upper case letter 'e'. For example, the number 5.033 x 10²³ is equivalent to 5.033E23 (or 5.033e23). For a very small number such as 6.674 x 10⁻¹¹ the E notation representation is 6.674E-11 (or 6.674e-11). You can read more about this convention in the scientific notation calculator.

When dealing with estimation, the number of significant digits should be no more than the log base 10 of the sample size and rounding to the nearest integer. For example, if the sample size is 150, the log of 150 is approximately 2.18, so we use 2 significant figures.

## Significant figures in mathematical operations

Let us consider the case when we obtain a result by performing mathematical operations on two or more variables. Any uncertainty in the measurement of the variables will also affect the uncertainty of the results.

For example, let us imagine that the measured mass of an object is $5.452\rm~ g$ (four significant figures), and its measured volume is $1.67~ \rm{cm^3}$ (three significant figures). Then, it would be irrelevant to express the density of this object as:

$\!\scriptsize density = \frac{mass}{volume} = \frac{5.452\rm~ g}{1.67~ \rm{cm^3}}\\ density = 3.26467065868\ \rm{g/cm^3}$

Since the actual measurements of mass and volume are less precise than what we express for the density, the above way of expressing the result is incorrect. The correct result is $3.26\ \rm{g/cm^3}$

In general, the number of significant figures in the calculated result is equal to the number of significant figures in the least precisely measured variable.

There are two rules regarding the arithmetic operations involving sig figs:

• For addition and subtraction operations, the result should have no more decimal places than the number in the operation with the least precision. For example, when performing the operation 128.1 + 1.72 + 0.457, the value with the least number of decimal places (1) is 128.1. Hence, the result must have one decimal place as well: 128.̲1 + 1.7̲2 + 0.45̲7 = 130.̲277 = 130.̲3. The position of the last significant number is indicated by underlining it.

• For multiplication and division operations, the result should have no more significant figures than the number in the operation with the least number of significant figures. For example, when performing the operation 4.321 × 3.14, the value with the least significant figures (3) is 3.14. So the result must also be given to three significant figures: 4.32̲1 × 3.1̲4 = 13.̲56974 = 13.̲6.

• If performing addition and subtraction only, it is sufficient to do all calculations at once and apply the significant figures rules to the final result.

• If performing multiplication and division only, it is sufficient to do all calculations at once and apply the significant figures rules to the final result.

• If, however, you do mixed calculations – addition/subtraction and multiplication/division – you need to note the number of significant figures for each step of the calculation. For example, for the calculation 12.1̲3 + 1.7̲2 × 3.̲4, after the first step, you will obtain the following result: 12.1̲3 + 5.̲848. Now, note that the result of the multiplication operation is accurate to 2 significant figures and, more importantly, one decimal place. You shouldn't round the intermediate result and only apply the significant digit rules to the final result. So for this example, the final steps of the calculation are 12.1̲3 + 5.̲848 = 17.̲978 = 18.̲0.

• Exact values, including defined numbers such as conversion factors and 'pure' numbers, don't affect the accuracy of the calculation. They can be treated as if they had an infinite number of significant figures. For example, when using the speed conversion, you need to multiply the value in m/s by 3.6 if you want to obtain the value in km/h. The number of significant figures is still determined by the accuracy of the initial speed value in m/s – for example, 15.23 × 3.6 = 54.83.

To use an exact value in the calculator, give the value to the greatest number of significant figures in the calculation. So for this example, you would enter 15.23 × 3.600 into the calculator.

Since we are talking about basic arithmetic operations, how about checking our distributive property calculator to learn how to handle complex mathematical problems that involve more than one arithmetic operation?

## Meet the creators of this significant figures calculator

Daniel, our experienced programmer, and Steve, our in-house physicist and expert in creating appealing scientific content, have been around since the early days of Omni Calculator. They conceived the idea for a significant figures calculator when discussing floating point integers in various programming languages and what it means in the real world.

Now, they use this tool frequently to ensure they're using the minimum number of digits after the decimal point in their calculations. More than anything, they're happy to share this tool with everyone who needs it.

A lot of effort goes into ensuring the quality of our content so that it is as accurate and reliable as possible. Each tool is peer-reviewed by a trained expert and then proofread by a native speaker. To learn more about our standards, please check the page.

## FAQ

### How many sig figs in 100?

100 has one significant figure (and it's a number 1). Why? Because trailing zeros do not count as sig figs if there's no decimal point.

### How many sig figs in 100.00?

100.00 has five significant figures. This is because trailing zeros do count as sig figs if the decimal point is present.

### How many sig figs in 0.01?

0.01 has one significant figure (and it's a number 1). Why? Because leading zeros do not count as sig figs.

### How many significant figures in the measurement of 0.00208 gram?

0.00208 has three significant figures (2, 0, and 8). Why? Because leading zeros do not count as sig figs, but zeroes sandwiched between non-zero figures do count.

### How many significant figures in the measurement of 100.10 in?

100.10 has five significant figures, that is, all its figures are significant. Why? Because the zeroes sandwiched between non-zero figures always count as sig figs, and there is the decimal dot, so the trailing zeros count as well.

### What is 2648 to three significant figures?

2648 to three significant figures is 2650.

### What is 2648 to two significant figures?

2648 to two significant figures is 2600.

Daniel Trojanowski and Steven Wooding
Enter number or expression (e.g. "5.13*3.78")
Number or expression
Round to sig fig (optional)
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