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Tools City

Significant Figures Calculator (Sig Fig Calculator)

Round a number to the nearest significant figure. Set the number of significant digits to round a number, decimal, or scientific notation with the help of this online free tool.

Enter number or expression (e.g. "5.13/3.78")

A sig fig calculator does a change over any number into another number with the desired amount of significant figures. It can also solve the expressions and give the outcome in the form of significant figures. Let's consider an expression 3.42/1.5+5.87; when we solve the expression by arithmetic rules, we get the answer 8.15, but in the sig fig calculator, we will get 8.2 because it will round off the digits.

What are the significant figures?

All measurements of physical quantities involve some degree of inaccuracy due to instrumental error and human error, etc. We must understand the limitations which experimental accuracy places on numbers that we measure.

Suppose the length of a body is recorded as 15.4 cm. This measurement approximates the nearest length, and its exam value lies between 15.35 and 15.45 cm. If the measurement is exact to the hundredth of a cm, it would have been recorded as 15.40 cm. The value 15.4 represents three significant figures (1, 5, 4), while the other 15.40 illustrates four significant figures (1, 5, 4, 0).

Thus a significant figure is the one that is known to the reasonably reliable.

How you can determine significant figures? Write its rules.

  • All the digits are significant figures except zero.

For example, we have the number 4917, which has four significant figures.

  • Zero digits that are in between non-zero digits will be counted as the significant figures.

For example, we have the number 32007 which has five significant figures.

  • All the zero digits that are located on the decimal point in a number less than one will not be considered as significant figures.

For example, the number 0.0003862 has only four significant figures that are 3, 8, 6, and 2.

  • The zeros that are located to the right of any decimal point will be considered as significant figures.

For example, we have the number 64.00 which has four significant figures.

  • 5. Zeros that are located on the decimal point in any number greater than unity are not necessarily significant figures.

For example, the number 460 has only two significant figures that are 4 and 6. In these cases, scientific notation is one of the most convenient ways for finding significant figures. Let's consider a certain distance of 1300000 cm is known to be five significant figures. If you write the number as 1300000 cm then it will create a problem because it implies that only two significant figures are known. In contrast, the scientific notation of the above number is 1.300 x 106 cm which has the advantage, indicating that the distance is known to four significant figures.

How does Tools City's Sig Fig calculator work?

Tools City's sig fig calculator can work in the two modes - performing arithmetic operations on multiple expressions or performing arithmetic operations on multiple numbers. Let us consider an expression 5.23/1.33. The result of the expression will show in the following way.

Decimal notation: 3.93

No. of significant figures: 3

No. of decimals: 2

Scientific notation: 3.93 × 100

E notation: 3.93e+0 

Now let us consider the number 0.12412. The result of the number will show in the following way.

Decimal notation: 0.12412

No. of significant figures: 5

No. of decimals: 5

Scientific notation: 1.2412 × 10-1

E notation: 1.2412e-1

Following the rules discussed above, we can calculate sig figs by hand or the significant figures counter. Consider the number 0.006275 and we want only two significant figures. The trailing zeros will be the placeholders, so we will not consider them as significant figures.

Next, we round 6275 to 2 digits, leaving us with 0.0063. Presently we'll consider an example that is anything but a decimal. Suppose we want this number 5,163,894 to 4 significant figures. We will round off the number to its nearest thousand, giving us 5,164,000.

What will happen if a number is written in scientific notation?

If any number is written in scientific notation, the same rules apply. First, you will enter the number, you will use E notation, replacing x 10 with either a lower or upper case letter 'E'. For example, the number 6.023x1012 is equivalent to 6.023e12. For a minimal number such as 3.604 x 10-11, the E notation representation is 3.604e-11.

When we access it, the number of significant digits ought to be close to the log base 10 with the sample size and round to the closest number. For example, if the size of a sample is 1500, the log of 1500 is approximately 3.17, so we use only two significant figures.

Significant figures in operations

There are many rules in significant figures to be followed for doing operations like addition, subtraction, multiplication, and division. 

  • The answer should have no more decimal places than the number in operation with the least precision for addition and subtraction. For example, when we add 728.1 + 2.78 + 0.527, the value with the least number of decimal places (1) is 728.1. Hence, the result must have at least one decimal place: 728.1 + 2.78 + 0.527 = 741.407 = 731.4.

  • There should not be more significant figures for multiplication and division in the result than the number in operations with the least significant figures. When you use any two numbers in calculations, significant figures in the answer will be limited to the number of significant figures in the original number. For example, a rectangular park with sides 9.5 m and 15.5 m has an area of 147.25 m2. However, one of these two original lengths is known to only two significant figures so, the final answer is limited with only two significant figures and it should be 150 m2.

  • The addition or subtraction of numbers that are expressed in scientific notations requires that they should be in the form of the same power of 10.

For example

2.25 x 106 + 6.4 x 107 = 2.25 x 106 + 64 x 106

2.25 x 106 + 6.4 x 107 = (2.25 + 64) x 106

2.25 x 106 + 6.4 x 107 = 66.25 x 106