Significant Figures

Subject: Compulsory Maths

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Overview

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

Significant Figures
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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

rules for significant counting
Rules for significant counting

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:

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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.
Questions and Answers

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.)

This is not useful answer.

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.

Quiz

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