Notes on Significant Figures | Grade 8 > Compulsory Maths > Real Number System | KULLABS.COM

Notes, Exercises, Videos, Tests and Things to Remember on Significant Figures

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• Note
• Things to remember
• Exercise
• Quiz

Numbers are often rounded to avoid reporting insignificant figures. Significant figures are often used in connecting with rounding.

Rounding 15.543 or 4.756 to 1 decimal place (d.p) seems sensible. The rounded figure is very close to an actual value.

15.543 = 15.5 (1 d.p)

4.756 = 4.8 (1 d.p)

But what happens if you round a very small number to 1 d.p?

0.00789 = 0.0 (1 d.p)

0.00456 = 0.0 (1 d.p)

This is not a useful answer. Another way to find an approximate answer with very small numbers is to use significant figures.

### Counting significant figures

Significant figures start at the first non-zero number, so ignore the zeros at the front, but not the ones in between. Look at the following examples:

0.0067 (Here, 6 is the first significant figure and 7 is the second significant figure)

0.0508 From the first significant figure onwards, all zeros are included. It's only the zeros at the beginning that don't count. Here, 5 is the first significant figure, 0-second significant figure and 8 is the third significant figure.

Examples

1. Round 0.0724591 to 3 significant figures, look at the fourth significant figure. It's a 5, so round up.
0.0724591
Therefore, 0.0724591 = 0.0725 (3 s.f.)

2. Round 0.2300105 to four significant figures.
Solution:
To round to four significant figures, look at the fifth significant figures.It's a 1, so round down.
0.2300105
Therefore, 0.2300105 = 0.2300 (4 s.f)
Even though 0.2300 is the same as 0.23, include the zeros to show that you have rounded to 4 significant figures.

• Significant figures include all digits except all leading zeros.
• Significant figures, sometimes do not always need to give a detailed answer to the problems.
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#### Click on the questions below to reveal the answers

Solution:

a) 5700

b) 5735

c) 4740

Here, 5735 is the nearest whole number to 5734.7

Solution:

i)2.007

ii)0.003

iii) 0.20

Here, 2.007 has 4 significant figures.

Solution:

i) 7.02 ii) 7.01 iii) 7.06

Here, 7.01 is the correct answer.

Solution:

12.756

= 12.8 ( 1 d.p)

Therefore, 12.756 = 12.8

Solution:

0.00456

=0.0

Therefore, 0.00456 = 0.0

Solution:

To round to 1 decimal place, look at the second decimal place, It's 4 and it is smaller than 5.So round up,

4.543 = 4.5(1 d.p.)

Therefore, 4.543 = 4.5(1 d.p.)

Solution:

0.00213

= 0.0 (1 d.p.)

Solution:

a) 4.6 b) 4.644 c) 4.64

Here, 4.644 is the correct answer.

Solution:

0.07245

=0.0725

Therefore, 0.07245 = 0.0725( 3 s.f)

Solution:

0.0037

=0.004(1 s.f)

Therefore, 0.0037 = 0.004.

0%
• ### Round 0.0524591 to 3 significant figures.

0.05244(3 s.f)
0.052459(3 s.f)
0.0525(3 s.f)
0.0524(3 s.f)
• ### Round 0.2300105 to four significant figures.

0.23001(4 s.f)
0.230011(4 s.f)
0.2300(4 s.f)
0.23002(4 s.f)

26
24
24.8
25

0.043
0.0433
0.0432
0.0432

7.06
7.02
7.01
7.05

0.334
0.335
0.333
0.3

0.8570
0.8571
0.8577
0.8572

3.01
2.9
3.0
3.03

3.7
3.64
3.5
3.6

0.00002
0.003
0.25
2.007

0.261
0.2601
0.2600
0.2608

45m
40m
50m
46m

5735
4740
5730
5700

0.0036
0.00359
0.0035
0.00358

0.0049
0.0047
0.00484
0.0048

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