Rounding

1
Rounding
Round to the nearest whole number
1.4
1.4 is clearly closer to 1 than 2 so it rounds
to 1
Round to the nearest whole number
1.5
Technically 1.5 is in the middle, but we always
round up 0.5 to the next whole number in this
case 2 (Integer)
Summary to round to the place value required
look to the number to the right
4 or less - the number stays the same (round down)
5 or more - the number increases by 1 (round up)
DO NOT CHANGE THE PLACE VALUE
2
Rounding
Examples
6 5 2 9 3 . 4
Look to the figure to the right It is 4 or less
so round down
Round to the nearest integer
65293
Look to the figure to the right It is 4 or less
so round down
Round to the nearest ten
65290
Look to the figure to the right It is 5 or more
so round up
Round to the nearest hundred
65300
Look to the figure to the right It is 4 or less
so round down
Round to the nearest thousand
65000
Round to the nearest ten thousand
Look to the figure to the right It is 5 or more
so round up
70000
3
Rounding
This also works for decimals
This number is said to have one decimal place (1
d.p.)
Definition
7.4
This number is said to have two decimal places
(2 d.p.)
10.36
This number is said to have three decimal places
(3 d.p.)
8.462
etc.
Examples
9.8 6 2 8 7
Look to the figure to the right It is 5 or more
so round up
Round to 1 decimal place
9.9
Look to the figure to the right It is 4 or less
so round down
Round to 2 d.p.
9.86
Look to the figure to the right It is 5 or more
so round up
Round to 3 d.p.
9.863
4
Rounding
Harder Example
6.99
Round to 1 d.p.
It is easier to see this on a number line
The first decimal place is tenths so if we look
in increments of one tenth
6.99
6.99 is now clearly closer to 7.0 than 6.9 so we
have to round up to 7.0
5
Rounding
Now answer these
Round these measurements to 1 decimal place (that
is, to the nearest millimetre). a) 18.67 cm b)
8.38 cm c) 68.23 cm d) 0.678 cm e) 0.4545 cm 6
Round these masses to 3 decimal places (that is,
to the nearest gram). a) 1.7683 kg b) 48.2467
kg c) 8.9247 kg d) 0.052905 kg e) 0.00035679 kg
18.7 cm
8.4 cm
68.2 cm
0.7 cm
0.5 cm
1.768 kg
48.247 kg
8.925 kg
0.053 kg
0.000 kg
6
Rounding
Rounding to the most significant figure
4 5 6 2
Which is the figure that describes the number the
best?
The thousand column has the most significant
figure
If I wanted to describe this number using only
one non zero figure (1.s.f.) it would be 5000
The hundred is the second most significant figure
If I wanted to describe this number using two non
zero figures (2 s.f.) it would be 4600 (round up
because the figure next to it is a 6)
Example 8624 write this number to
1 s.f.
9000
2 s.f.
8600
4 s.f.
8624
3 s.f.
8620
7
Rounding
Now answer these

• 1. Round these numbers to one significant figure.
• 326 b) 589 c) 3245
• Round these numbers to two significant figures.
• d) 9999 e) 9099 f) 9950
• 2. Round these numbers to one significant figure.
• 4.826 b) 0.4826 c) 0.04826 d) 0.004826
• Round these numbers to two significant figures.
• e) 0.0004826 f) 0.00004826

3000
300
600
10000
10000
9100
0.5
0.05
5
0.005
0.00048
0.000048
8
Estimating
If I went to the shop and wanted 5 litres of milk
and I saw the price at 0.96 I would think that I
would need about 5
I have rounded 0.96 to 1 s.f. 1 and
multiplied it by 5 to 5
Why?
Estimating can be done simply by rounding to the
nearest significant figure
Examples
Round each number to 1 s.f.
9.58 x 2.73
10 x 3
Estimated answer 30
Actual answer 26.1534
Round each number to 1 s.f.
Calculate the Numerator first
Estimated answer 400
Actual answer 39.3897
9
Estimating
Now try these
0.2 x 6 1.2
8 5 13
90 x 6 540 1700 0.3 0.3
20 x (8-4) 80
50
240
8
640
100
81
280
10
Upper Lower Bounds
What could be the highest this number could be if
it has already been rounded to the nearest 10?
70
74 would be rounded down to 70 but 75 would be
rounded up to 80
Therefore the highest the number could be before
rounding is 74
What could be the lowest this number could be if
it has already been rounded to the nearest 10?
70
65 would be rounded up to 70 but 64 would be
rounded down to 60
Therefore the lowest the number could be before
rounding is 65
11
Upper Lower Bounds
Now try these

• 1. Each of these quantities is rounded to the
  nearest whole number
• of units. Write down the minimum and maximum
  possible size of each quantity.
• 26 g b) 4 cm c) 225 m
• d) 13 litres e) 33 kg f) 249

4.4 cm 3.5 cm
225.4 m 224.5 m
26.4 g 25.5 g
12.4 g 12.5 g
33.4 kg 32.5 kg
249.50 248.49
3. A packet weighs 2 kg, correct to the nearest
100 g. What is the maximum possible weight?
2.049 kg
5. The weight of a toffee is 5 g correct to the
nearest half gram. What is the minimum possible
weight of one toffee?
4.75 g