What are Significant Figures? | Physics for EmSAT Achieve PDF Download

What Are Significant Figures?

• Significant figures (or significant digits) are the number of digits in a given value or a measurement, necessary to decide the accuracy and precision of measurement.
• They are important in scientific or technical measurements.
• “Significant” means important. They refer to the reliable digits in the given number, which are sufficient to convey accurate information. They also help us round off measurement values or the outcome of a calculation. 

Significant Figures Definition

• Significant figures (or significant digits) are the number of digits important to determine the accuracy and precision of measurement, such as length, mass, or volume.
• Significant digits in math convey the value of a number with accuracy. They are considered substantial figures that contribute to the precision of a number.

What Are the Rules for Significant Figures?

Certain rules help us determine the number of significant figures. These rules are as follows: 

(1) All non-zero digits are significant.
How many significant figures in 20? Two!

• 652.1 miles -4 significant figures.
• 3.4 inches -2 significant figures.

(2) All zeros in between non-zero digits are significant.

•  23.0041 -6 significant digits. 
• 4005 feet -4 significant digits.

(3) Zeros on the right of a decimal point and before (or to the left of) the first non-zero digit are not significant. They only represent the position of the decimal point.

• 0.003 -1 significant digit. 
• 0.0034 - 2 significant digits

(4) Zeros on the right of a decimal point are significant, provided there is no non-zero digit after them.

• 7.00 -3 significant digits. 

(5) Zeros on the right of the last non-zero digit after a decimal point are significant. So, final zeros or trailing zeros in the decimal part are significant.

• 0.6500 -4 significant digits
• 12.300 -5 significant digits

(6) In a measurement value, zeros that occur on the right of the last non-zero digit are significant.

• 2650 inches -4 significant digits

How to Round off Significant Figures

To round off significant figures, we have to omit one or more digits from the right side of the number until we reach the number of significant digits that we want to round it off to.
First, we have to look at the digit on the right end of the number (to the right of the digit we want to round it off to).

• If the digit is lower than 5, the number is rounded off to the lower number.
•  If the digit is greater than or equal to 5, the number is rounded up to the higher number.

If there is more than one digit on the left, the number will be rounded off as a whole and not digit by digit.

Example: How many significant figures are there in 0.04582? Four! The four significant digits are 4, 5, 8, and 2. 

Let’s round off this number to three significant digits.
Check the last digit, which is 2.
We will round it to 0.0458 since the last digit, 2, is less than 5.
If we want to round it off further to 2 significant digits, then it will be rounded up to 0.046 because the last digit, 8, is greater than 5. 

Here’s an example of a decimal rounded from 6 significant digits to 1 significant digit:

Multiplication and Division with Significant Figures

When multiplying and dividing significant figures, we follow the given steps. 

• Identify significant digits of each number.
• Find the least number of significant digits in any of the numbers.
• Multiply or divide the numbers in the problem as you would normally.
• Once you get the product or quotient, round off the number so it does not have more significant digits than the number with the least significant digits.

The LEAST number of significant figures in the given numbers determines the number of significant figures in the answer. 

Example: 1.4 x 2 = 2.8

1.4: 2 significant digits and 2: 1 significant digit

Least number of significant digits = 1
So, we round 2.6 to 3 since the last digit 6 > 5

Addition and Subtraction with Significant Figures

• For each number, check the number of significant figures to the right of the decimal point (in the decimal part).
• Identify the LEAST number of significant digits.
• Add or subtract the numbers in the usual manner.
• When you get the final sum or difference, round off the number so that it does not have more significant digits on the right of the decimal point than the least number you found earlier.

Example: Add 3.240 inches and 8.12 inches.

Here, 3.240: 3 significant figures in the decimal part
8.12: 2 significant figures in the decimal part
Adding two decimals, we get

3.240 + 8.12 = 11.360, which has 3 significant digits in the decimal part.
So, we round it off to two significant figures to get 11.36.