Significant figures

Significant figures: Definition, Rules, and Calculation

In mathematics, a significant figure is used to measure how precise a number is. While representing a number in numerical, it is necessary to include the correct number of significant figures. It is widely used in mathematics, statistics, physics, Finance, and many other branches of science where we are calculating things to a certain level of accuracy.

In this post, we will learn about the definition, rules, and how to calculate the significant figures along with a lot of examples.

Significant Figures

Significant figures of a number are digits in the number that is valid and really required to expose the amount of something. Or 

Significant figures are the number of digits in a value, frequently a measurement, that provides the degree of accuracy (refers to how carefully person measurements trust a real or accurate value) of the value. 

In simple words, the digits of a number or a cost that make a distinction when used in any calculation are known as significant figures.  Significant figures are also called significant digits.

Significant figures

Rules of Significant Figures

There are some rules of significant figures that are necessary to make the number significant. Let us discuss them briefly.

  1. Non-zero Digits

All the digits that are non-zero in a number, no problem (matter) at which location they are, are significant. For example,

9.9 has 2 sig fig.

298 has 3 sig fig.

123456 has 6 sig fig.

  1. Zero between Non-zero digits

The zeros are also significant that are present among or between two non-zero digits or two significant digits. For example,

909 has 3 sig fig.

290008 has 6 sig fig.

12340056 has 8 sig fig.

  1. Trailing zeros with no decimal point

If the number is without any decimal point or has no decimal point, trailing zeros are ignored and should be insignificant. For example,

23000 has 2 sig fig.

34500 has 3 sig fig.

4567000 has 4 sig fig.

  1. Trailing zeros with a decimal point

If the number has a decimal point, then the trailing zeros are significant and should be counted. For example,

23.000 has 5 sig fig.

34.5100 has 6 sig fig.

45.67000 has 7 sig fig.

  1. Leading zeros

The zeros which are present at the left side of a number before any non-zero digit or significant figure should be ignored and are considered insignificant. For example,

0.000034 has 2 sig fig.

0.001010 has 4 sig fig.

0.000009 has 1 sig fig.

You can also use an online Significant Figures Calculator to verify these results.

How to calculate Significant Figures?

To calculate the significant figure, keep the rules in mind and make a list of the rules and learn all the rules in order to solve the significant figures accurately. Let us make the list of rules.

  1. All the numbers that are non-zero are significant.
  2. The zeros are also significant that are present between two non-zero digits or two significant digits.
  3. Leading zeros should be ignored and considered as insignificant.
  4. If the number is without any decimal point, trailing zeros are ignored and should be insignificant.
  5. If the number has a decimal point, then the trailing zeros are significant and should be counted.

In order to learn how to calculate the significant figures let us take some examples.

Example 1

Find the significant figures of the following numbers.

  1. 34506
  2. 201.3
  3. 0.098010

Solution 

Step 1: 34506

Each digit is significant.

Number of sig fig = 5

Step 2: 201.3

Each digit is significant.

Number of sig fig = 4

Step 3: 0.098010

9, 8, 0, 1, and 0 are significant as leading zeros are insignificant.

Number of sig fig = 5

Example 2

Find the significant figures of the following numbers.

  1. 5670000
  2. 100.000
  3. 90000009

Solution 

Step 1: 5670000

5, 6, and 7 are significant as trailing zeros are insignificant.

Number of sig fig = 3

Step 2: 100.000

Each digit is significant as trailing zeros with a decimal point is significant.

Number of sig fig = 6

Step 3: 90000009

Each digit is significant as zeros between significant figures are also significant.

Number of sig fig = 8

Example 3

Find the significant figures of the following numbers.

  1. 0.00005670000
  2. 100000
  3. 0.0000009

Solution 

Step 1: 0.00005670000

5, 6, 7, 0, 0, 0, and 0 are significant as leading zeros are insignificant.

Number of sig fig = 6

Step 2: 100000

Only 1 is significant as trailing zeros without any decimal point or no decimal point is insignificant.

Number of sig fig = 1

Step 3: 0.0000009

Only 9 is significant as leading zeros are ignored and should be insignificant.

Number of sig fig = 1

Round to significant figures

We can round the significant figures to any decimal place as round to 1 significant figure, round to 2 significant figures, and so on. To round significant figures along with sig fig calculation, sig figs calculator could be a very handy tool if you want to save your time.

Round is a basic rule that how many digits we want as if we want three digits, look at the 4th digit if it is 5 or greater than 5 increase the 3rd digit, or if the 4th digit is less than 5 then the 3rd digit remains the same and all the digits after 3rd should be ignored or considered as zero. This form can apply to any decimal place.

Let us take some examples to understand round to significant figures.

Example 1

Find round to significant figures up to two places of the following numbers.

  1. 34506
  2. 201.3
  3. 0.098010

Solution 

Step 1: 34506

In this number, we want round to sig fig for two places, as the 3rd digit is 5 so we increase the 2nd digit. And all the digits after 2 places are considered as zeros

34506 = 35000 

So, the sig fig is 3 and 5.

Step 2: 201.3

In this number, we want round to sig fig for two places, as the 3rd digit is less than 5 so the 2nd digit remains the same. And all the digits after 2 places are considered as zeros.

201.3 = 2000

So, the sig fig is 2.

Step 3: 0.098010

In this number, we want round to sig fig for two places, as the 3rd digit is less than 5 so the 2nd digit remains the same. And all the digits after 2 places are considered as zeros.

0.098010 = 0.098

So, the sig fig is 9 and 8.

Summary 

Significant figures are used to measure how precise a number is. Significant figures follow some basic rules and sig fig is easily calculated by following these rules. Sig fig can also be rounded. Now you are witnessed, this topic is not difficult. Once you grab the basic concepts of this topic you can easily solve the problems related to sig fig.

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By Michael Caine

Michael Caine is the Owner of Amir Articles and also the founder of ANO Digital (Most Powerful Online Content Creator Company), from the USA, studied MBA in 2012, love to play games and write content in different categories.

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