Title: Significant figures.

Objective:

At the end of this lesson, you'll be able to round off numbers to a given significant figure(s).

What you should know:

Any digit ranging from 0 to 4 is changed to 0 while any digit ranging from 5 to 9 is changed to 1.

Introduction:

Significant figures in mathematics refer to the place value of digits that are important in a given number, this is done by changing the next digit after the significant figure(s) to either 0 or 1, that is, if the next digit ranges from 0 to 4 or 5 to 9 respectively and it is added to the significant figures.

Presentation/ Steps:

Let's treat some examples to have a better understanding of this lesson.

1. Round off 415 to 2 significant figures.

Steps:

=> 41 are the significant figures (digits).

=> The next digit after 41 is 5.

=> 5 will change to 1 and be added to 41 + 1 = 42.

=> After the addition, 5 will change to 0, i.e. 420.

=> Therefore, 415 to 2 S.F = 420.

2). Round off 625.93 to (i) 1 significant figure (ii) 2 significant figures (iii) 3 significant figures (iv) 4 significant figures.

N. B:

The above example has decimal places and in dealing with decimals, the digits after the decimal point are not significant unless you are asked to round off to a significant figure that spans up to the decimal numbers.

Step1: 625.93 to 1 S.F

=> The 1 S.F. is 6.

=> The next digit after 6 is 2.

=> 2 will change to 0 and be added to 6, 6 + 0 = 6.

=> Every digit after 6 will change to 0 and the 0s after the decimal point will be neglected,

600.00.

=> Therefore, 625.93 to 1 S.F = 600.

Step2: 625.93 to 2 S.F

=> The 2 S.F. are 62.

=> The next digit after 62 is 5.

=> 5 will change to 1 and be added to 62, 62 + 1 = 63.

=> Every digit after the significant figures will change to 0 and the 0s after the decimal point will be neglected, 630.00.

=> Therefore, 625.93 to 2 S.F = 630.

Step3: 625.93 to 3 S.F

=> The 3 S.F. are 625.

=> The next digit after 625 is 9.

=> 9 will change to 1 and be added to 625, 625 + 1 = 626.

=> Every digit after the significant figures will change to 0 and the 0s after the decimal point will be neglected, 626.00.

=> Therefore, 625.93 to 3 S.F = 626.

Step4: 625.93 to 4 S.F

=> The 4 S.F. are 625.9.

=> The next digit after 625.9 is 3.

=> 3 will change to 0 and be added to 625.9,

625.9 + 0 = 625.9.

=> The digit after 9 will change to 0 and it will be neglected, 625.90.

=> Therefore, 625.93 to 4 S.F = 625.9

3). Round off 0.0031752 to 2 S.F

=> In this example after the decimal point are not significant, so the next 2 digits are the significant figures.

=> The next digit after 31 is 7.

=> 7 will change to 1 and be added to 31, 31 + 1 = 32.

=> Every digit after the significant figures will change 0 and the 0s after the significant figures will be neglected, 0.0032000.

=> Therefore, 0.0031752 to 2 S.F = 0.0032.

Summary / Conclusion :

Significant figures are also written as S.F.

If you're asked to leave your answer to any mathematical problem to a given significant figure(s), the round-off should be done on the final result.

Exercise :

Round off the following to 2 S.F (a) 99.6 (b) 0.963 (c) 5.789.