Rounding
Round to the nearest whole number
2
1
1.4
Round to the nearest whole number
1
1.5
1.4
1.4 is clearly closer to 1
than 2 so it rounds to 1
1.5
Technically 1.5 is in the
2 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
Rounding
Examples:
65293.4
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
to the figure to the right
Round to the nearest thousandLook
It is 4 or less so round down
65000
Round to the nearest ten
thousand
70000
Look to the figure to the right
It is 5 or more so round up
Rounding
This also works for decimals
Definition:
7.4
This number is said to have
one decimal place (1 d.p.)
This number is said to have
two decimal places (2 d.p.)
10.36
8.462
This number is said to have
three decimal places (3 d.p.)
etc.
Examples:
9.8 6 2 8 7
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
Rounding
Harder Example
6.99
Round to 1 d.p.
It is easier to see this on a number line
The first decimal
6.99
place is tenths so
if we look in
increments of one tenth
6.8
6.9
7.0
7.1
6.99 is now clearly closer to 7.0 than 6.9 so we have to round up to 7.0
Rounding
Now answer these:
Round these measurements to 1 decimal place
(that is, to the nearest millimetre).
18.7 cm
a) 18.67 cm
b) 8.38 cm
8.4 cm
c) 68.23 cm
68.2 cm
d) 0.678 cm
0.7 cm
e) 0.4545 cm
0.5 cm
6 Round these masses to 3 decimal places (that is, to the
nearest gram).
1.768 kg
a) 1.7683 kg
b) 48.2467 kg
48.247 kg
c) 8.9247 kg
8.925 kg
d) 0.052905 kg
0.053 kg
e) 0.00035679 kg 0.000 kg
Rounding
Rounding to the most significant figure
4562
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
3 s.f.
8620
2 s.f.
8600
4 s.f.
8624
Rounding
Now answer these:
1. Round these numbers to one significant figure.
a) 326
b) 589
c) 3245
3000
300
600
Round these numbers to two significant figures.
d) 9999
e) 9099
f) 9950
10000
10000
9100
2. Round these numbers to one significant figure.
a) 4.826
b) 0.4826
c) 0.04826
d) 0.004826
0.5
5
0.05
0.005
Round these numbers to two significant figures.
e) 0.0004826
f) 0.00004826
0.00048
0.000048
Estimating
If I went to the shop and wanted 5 litres of milk and I
saw the price at $1.96 per litre I would think that I would need
about $10. Why?
I have rounded $1.96 to 1 s.f. ($2) and multiplied it by 5 to $10
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
Calculate the
Numerator first
62.3 x 78.4 Round each number to 1 s.f.
124
Estimated answer 400
4800
120
Actual answer 39.3897
60 x 80
120
Estimating
Now try these
8 + 5 = 13
8
2 = 4
0.2 x 6 = 1.2
=50
=8
=100
=81
=280
90 x 6 = 540 = 1700
0.3
0.3
20 x (8-4) = 80
=240
=640
=96  0.3
or 960
3 = 320
Upper & Lower Bounds
What could be the highest this number could be if it
has already been rounded to the nearest 10?
60
70
80
90
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
70
80
90
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
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.
4.4 cm
225.4 m
26.4 g
a) 26 g 25.5 g
b) 4 cm 3.5 cm c) 225 m224.5 m
12.4 g
d) 13 litres 12.5 g
33.4 kg
e) 33 kg 32.5 kg
$249.50
f) $249 $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