Significant Figures Calculator - Sig Fig

By Daniel Trojanowski and Steven Wooding
Last updated: Aug 04, 2021

The significant figures calculator converts any number into a new number with the desired amount of sig figs AND solves expressions with sig figs (try doing 3.14 / 7.58 - 3.15). What are the significant figures rules? Those concepts will be explained throughout this page as well as how to use a sig fig calculator.

What are significant figures?

Significant figures are all numbers that add to the meaning of the overall value of the number. 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.

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 the 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 which are not significant but are not removed, as removing 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.

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 x 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).

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 operations

There are additional rules regarding the operations - addition, subtraction, multiplication, and division.

  • 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.

FAQ

How many sig figs in 100?

100 has one significant figure (and it's figure 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 (and it's figure 1). Why? 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 figure 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
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