1. Rounding
Round to the nearest whole number
1.4
1.4 is clearly closer to 1
than 2 so it rounds to 1 1
1.4 2
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) 1
1.5 2
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. Round to the nearest integer 65293
Rounding
Examples:
Round to the nearest integer
Look to the figure to the right
It is 4 or less so round down
65293
Round to the nearest ten
Look to the figure to the right
It is 4 or less so round down
65290
Round to the nearest hundred
Look to the figure to the right
It is 5 or more so round up
65300
Round to the nearest thousand
Look to the figure to the right
It is 4 or less so round down
65000
Round to the nearest ten
thousand
Look to the figure to the right
It is 5 or more so round up
70000

3. This also works for decimals Definition: 7.4
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:
Round to 1 decimal place
Look to the figure to the right
It is 5 or more so round up
9.9
Round to 2 d.p.
Look to the figure to the right
It is 4 or less so round down
9.86
Round to 3 d.p.
Look to the figure to the right
It is 5 or more so round up
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
6.8
7.1
7.0
6.9
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) cm
b) 8.38 cm
c) cm
d) cm
e) cm
6 Round these masses to 3 decimal places (that is, to the nearest gram).
a) kg
b) kg
c) kg
d) kg
e) kg
18.7 cm
8.4 cm
68.2 cm
0.7 cm
0.5 cm
1.768 kg kg
8.925 kg
0.053 kg
0.000 kg

6. Rounding
Rounding to the most significant figure
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
write this number to:
1 s.f.
9000
2 s.f.
8600
3 s.f.
8620
4 s.f.
8624

7. Rounding
Now answer these:
1. Round these numbers to one significant figure.
326 b) c) 3245
Round these numbers to two significant figures.
d) e) f) 9950
2. Round these numbers to one significant figure.
b) c) d)
e) f)
300
600
3000
10000
9100
10000 5
0.5
0.05
0.005

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
Why?
I have rounded £0.96 to 1 s.f.
£1 and multiplied it by 5 to £5
Estimating can be done simply by rounding to the nearest
significant figure:
Examples
9.58 x 2.73
Round each number to 1 s.f.
10 x 3
Estimated answer 30
Actual answer
62.3 x 78.4
124
Round each number to 1 s.f.
60 x 80
120
Calculate the
Numerator first
Estimated answer 400
4800
120
Actual answer

9. Estimating Now try these =50 =240 =8 =640 =100 =81 =280 =96 0.3
8 + 5 = 13
0.2 x 6 = 1.2
90 x 6 = 540 = 1700
20 x (8-4) = 80
=50
=240
= 4 =8
=640
=100
=81
=280 =
or = 320

10. Upper & Lower Bounds
What could be the highest this number could be if it
has already been rounded to the nearest 10? 60 90 80 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? 60 90 80 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
26.4 g
25.5 g
4.4 cm
3.5 cm
225.4 m
224.5 m
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