Transcript rounding
Rounding
Round to the nearest whole number 1.4
1 1.4
2 Round to the nearest whole number 1.4 is clearly closer to 1 than 2 so it rounds to 1 1.5
1 1.5
2 Technically 1.5 is in the middle, but we always round up 0.5 to the next
Summary
whole number in this case 2 (Integer) 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: 6 5 2 9 3 . 4 Round to the nearest integer Round to the nearest ten Look to the figure to the right It is 4 or less so round down Look to the figure to the right It is 4 or less so round down Round to the nearest hundred Look to the figure to the right It is 5 or more so round up Round to the nearest thousand Look to the figure to the right It is 4 or less so round down Round to the nearest ten thousand Look to the figure to the right It is 5 or more so round up 65293 65290 65300 65000 70000
Rounding
This also works for decimals Definition: 7.4
10.36
This number is said to have one decimal place (1 d.p.) This number is said to have two decimal places (2 d.p.) 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 Round to 2 d.p.
Round to 3 d.p.
Look to the figure to the right It is 5 or more so round up Look to the figure to the right It is 4 or less so round down Look to the figure to the right It is 5 or more so round up 9.9
9.86
9.863
Rounding
Harder Example 6.99
Round to 1 d.p.
It is easier to see this on a number line 6.99
6.8
6.9
7.0
7.1
The first decimal place is tenths so if we look in increments of one tenth 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).
a) 18.67 cm
18.7 cm
b) 8.38 cm c) 68.23 cm d) 0.678 cm e) 0.4545 cm
8.4 cm 68.2 cm 0.7 cm 0.5 cm
6 Round these masses to 3 decimal places (that is, to the nearest gram).
a) 1.7683 kg b) 48.2467 kg
1.768 kg 48.247 kg
c) 8.9247 kg d) 0.052905 kg e) 0.00035679 kg
8.925 kg 0.053 kg 0.000 kg
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 3 s.f.
8620 2 s.f.
4 s.f.
8600 8624
Rounding
Now answer these: 1. Round these numbers to one significant figure.
a) 326
300
b) 589
600
c) 3245
3000
Round these numbers to two significant figures.
d) 9999
10000
e) 9099
9100
f) 9950
10000
2. Round these numbers to one significant figure.
a) 4.826 b) 0.4826 c) 0.04826 d) 0.004826
5 0.5
0.05
Round these numbers to two significant figures.
e) 0.0004826 f) 0.00004826
0.005
0.00048
0.000048
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 10 x x 2.73
3 Round each number to 1 s.f.
Estimated answer 30 Actual answer 26.1534
Calculate the Numerator first 62.3 x 78.4
124 4800 120 Round each number to 1 s.f.
Estimated answer 400 Actual answer 39.3897
60 x 80 120
Estimating
Now try these
8 + 5 = 13
=
100
=
81
0.2 x 6 = 1.2
=
50 =8
=
280
90 x 6 = 540 = 1700 0.3 0.3
20 x (8-4) = 80
=
240 =640
= or
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.
26.4 g
a) 26 g
25.5 g
b) 4 cm
4.4 cm 3.5 cm
c) 225 m
225.4 m 224.5 m
d) 13 litres
12.4 g 12.5 g
e) 33 kg
33.4 kg 32.5 kg
f) £249
£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?