Note on Significant Figures

  • Note
  • Things to remember
  • Exercise
  • Quiz

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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:

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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Very Short Questions

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.)

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.

0%
  • Round 0.0524591 to 3 significant figures.

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

    0.23001(4 s.f)
    0.2300(4 s.f)
    0.23002(4 s.f)
    0.230011(4 s.f)
  • Round off the following numbers to the significant figures.

    24.7(2 s.f)

    24.8
    26
    24
    25
  • Round off the following numbers to the significant figures.

    0.0432 (2 s.f)

    0.043
    0.0432
    0.0432
    0.0433
  • Round 7.00521 to 3 s.f

    7.01
    7.06
    7.05
    7.02
  • Express (frac{1}{3}) in decimal upto 3 s.f.

    0.334
    0.3
    0.335
    0.333
  • Express (frac{6}{7}) in decimal upto 4 s.f.

    0.8570
    0.8571
    0.8572
    0.8577
  • Round 2.99 to 2 s.f.

    3.01
    3.0
    3.03
    2.9
  • Round 3.643 to 2 decimal number.

    3.7
    3.64
    3.5
    3.6
  • Which number has 4 significant figures?

    0.003
    0.00002
    0.25
    2.007
  • Round off the following numbers to the Significant figures.

    0.2607 (3 s.f)

    0.2608
    0.2600
    0.261
    0.2601
  • Round 45.53m to the nearest ten meters.

    40m
    46m
    45m
    50m
  • Round 5734.7 to the nearest whole number.

    5700
    5735
    5730
    4740
  • Round off the following numbers to the Significant figures.

    0.00357 (2 s.f)

    0.00359
    0.0035
    0.00358
    0.0036
  • Round off the following numbers to the Significant figures.

    0.00483 (2 s.f)

    0.0048
    0.0047
    0.00484
    0.0049
  • You scored /15


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