 ## Significant Figures

Subject: Compulsory Maths

#### Overview

The significant figures of a number are digits that carry meaning contributing to its measurement resolution.

##### Significant Figures

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.
##### Things to remember
• Significant figures include all digits except all leading zeros.
• Significant figures, sometimes do not always need to give a detailed answer to the problems.
• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.

Solution:

1. 0.3007 has four significant figures.
2. 2.01 has three significant figures.
3. 0.001023 has four significant figures.

Solution:

To, round to four significant figures, look at the fifth significant figure. It's a 1, so round down,

 0. 2500107

Therefore, 0.2500107 = 0.2500 (4 s.f)

Even though 0.2500 is the same as 0.25, include the zeros to show you have rounded to 4 significant figures.

Solution:

To round to second significant figures, look at the third significant figure. It's 3, so round down,

 0.043

Therefore, 0.0433 = 0.043 ( 2 s.f)

Solution:

To round to three 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)

Solution:

To round to 3 significant figures, look at the fourth significant figure. It's 7, so round down,

 0.2607

Therefore, 0.2607 = 0.261 (3 s.f)

Solution:

To round to four significant figures, look at the fifth significant figure. It's 6, so round down,

 324.064

Therefore, 324.064 = 324.100

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:

To round to four significant figures, look at the fifth significant figures. It's 6, so round down,

 2.00456

Therefore, 2.00456 = 2.0046

Solution:

To round to three significant figures, look at the fourth significant figure. It's a 7, so round down,

 0.2607

Therefore, 0.2607 = 0.261

Solution:

i) 7.02 ii) 7.01 iii) 7.06

Here, 7.01 is the correct answer.

Solution:

To round to three significant figures, look at the fourth significant figures. It's a5, So round down,

 2.055

Therefore, 2.055 = 2.06 (3 s.f)

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.