apt4Maths
Minimising Workloads
Maximising Performance
GCSE (& Key Stage 3)
MATHEMATICS
Number
Place Value and Approximations
Approximations - Decimal Places
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Lesson Objectives
• To teach you techniques for
approximating to a fixed number of
decimal places.
© APT Initiatives Ltd, 2019
Decimal Places
• To approximate means to give a rough estimate, not
an exact value.
• The symbol ‘≈’ means approximately equal to.
• Decimal places (d.p.) are the number of digits you
must have in your final answer after the decimal
point.
• Truncate means to cut off at a particular point
(everything on the right become zeros or is ignored
as appropriate).
© APT Initiatives Ltd, 2019
Approximating to Decimal Places
• Imagine the decimal number you have been given
truncated (ie cut off) after the specified number of decimal
places.
• Now look at the next number to this on a number line (ie
the last digit of your truncated value would be 1 bigger).
• Which of these two values is your original value closest to?
• If the digit on the right (called the decider) of the required
number of decimal places is 5 or more, round UP,
otherwise your truncated value is your answer.
© APT Initiatives Ltd, 2019
Example 1
Give 3.67083 to 2 d.p.
Truncated:
Next value:
3.67
3.68
Which is 3.67083 closest to?
This ‘0’ is less than 5 so stick with the truncated value
3.67083 approximates to 2 d.p. is 3.67
© APT Initiatives Ltd, 2019
Example 2
Give 24.7728 to 1 d.p.
Truncated:
Next value:
24.7
24.8
Which is 24.7728 closest to?
This ‘7’ is more than 5 so round UP to the next value
24.7728 approximates to 1 d.p. is 24.8
© APT Initiatives Ltd, 2019
Practice
Round each value to the number of d.p. quoted in brackets:
1)
4.873
(1 d.p.)
2)
0.7942
(2 d.p.)
3)
2.3549
(1 d.p.)
4)
5.12741 (3 d.p.)
5)
7.0663
(1 d.p.)
6)
4.4971
(2 d.p.)
Work out YOUR
answers FIRST, then
click on to the next
slide to check them.
© APT Initiatives Ltd, 2019
Answers
1)
4.873
(1 d.p.)

4.9
2)
0.7942
(2 d.p.)

0.79
3)
2.3549
(1 d.p.)

2.4
4)
5.12741 (3 d.p.)

5.127
5)
7.0663
(1 d.p.)

7.1
6)
4.4971
(2 d.p.)

4.50
© APT Initiatives Ltd, 2019
What next?
• It would be wise to make some notes and write
down some examples.
• We haven’t really done many practice questions
so you may like to do a few more.
• You could now move on to look at approximating
to a particular number of significant figures.
© APT Initiatives Ltd, 2019