Access Number Sheet 6
Most calculators display answers of up to 10 digits. In most cases, this is too many digits.
Therefore it is necessary to give an approximate answer which contains fewer digits.
Rounding numbers Round these numbers to the nearest £10
Giving the complete number for something is sometimes unnecessary. For instance, the attendance at a football match might be 23745. But for most people who want to know the attendance figure, an answer of 'nearly 24000', or 'roughly 23700', is fine.
7 £82
8 £176
9 £181
10 £292.50
11 £475.85
12 £3854
Round these numbers to the nearest £1
We can round off large numbers like these to the nearest thousand, nearest hundred, nearest ten, nearest whole number, or any other specified number.
13 £45.69
14 £72.85
15 £31.10
Decimal Places
16 £173.55
17 £273.99
18 £644.85
Often you are asked to write an answer to a given number of decimal places.
Count the number of decimal places you need.
Round 23745 to the nearest thousand.
First, look at the digit in the thousands place. It is 3. This means the number lies between 23000 and 24000. Look at the digit to the right of the 3. It is 7. That means 23745 is closer to 24000 than
23000.
Remember - The rule is, if the next digit is: 5 or more, we 'round up'. 4 or less, it stays at it is.
23745 to the nearest thousand = 24000.
23745 to the nearest hundred = 23700.
EXERCISE 1
Round these numbers to the nearest
£100
1 £598
2 £602
3 £730
4 £890
5 £1520
6 £23890
Look at the next digit. If it’s 4 or below just write down the answer with the right amount of decimal places. If it’s 5 or above write down the number but put your last decimal place up by one.
For example: 2.3635 to two decimal places
For example: 53.586 to two decimal places
What if the last digit is a 9?
A 9 goes up to a 10 so you need to put a zero in the last column and add one to the previous number.
For example: 8.6397 to three decimal places

EXERCISE 2
Put these numbers correct to
a two decimal places
b one decimal place
1 2.211
2 5.792
3 9.353
4 8.124
5 1.235
6 2.286
7 5.717
8 9.328
9 8.199
10 1.260
Significant Figures
The first significant figure in a number is the first non-zero digit (reading from left to right).
The remaining digits to the right are all significant figures.
The diagram below shows the significant figures in the numbers 302.150 and
0.005106
Examples
Round these numbers to the specificed number of significant figures:
(a) 523.591 to 4 significant figures
(1) First we place the cut-off point after the 4th significant figure:
(2) The digit after the cut-off point is 5 or more, so the digit before it is increased by 1:
5 2 3 . 5|9 1
5 2 3 . 6|9 1
(3) The digits after the cut-off point are removed:
5 2 3 . 6|
(4) There are no gaps to fill between the cut-off point and the dec point, so our answer is:
5 2 3 . 6
(4 s.f.)
(b) 3441.5 to 2 significant figures
(1) First we place the cut-off point after the 2nd significant figure:
(2) The digit after the cut-off point is not 5 or more, so the digit before it is unchanged:
(3) The digits after the cut-off point are removed (but not the decimal point):
3 4|4 1 . 5
3 4|4 1 . 5
3 4|_ _ . _
(4) The gaps between the cut-off point and the decimal point are filled with zeroes, giving:
3 4 0 0
(2 s.f.)
EXERCISE 3
Give the following numbers to
a two significant figures
b one significant figure
1 654.389
2 65.4389
3 654389
4 56.7688
5 0.03542210
6 0.0041032
Estimating
You should always do a quick estimate in your head when doing arithmetic so you can see if your answer is reasonable.
Generally, you should round each number involved to one significant figure and then it’s easy to estimate by using the single digits and moving the point around.
E.G. 936 x 27 - this is difficult to do in your head but if we round both numbers to
one significant figure it becomes 900 x
30.
Now this is easy to do in your head by doing
9 x 3 = 27 then moving the point 3 times
(putting three noughts on!) giving the answer 27 000 which is a good estimate of the real answer 25 272.

Here’s some more!
45 x 72 becomes 50 x 70 which is 3500
317 x 23 becomes 300 x 20 which is 6000
Always check that your estimates are reasonable answers!
EXERCISE 4
First make a rough estimate and then perform these calculations accurately.
Put your answers into a table.
1 Find the total lengths of 9 beds each of length 1.9 metres.
2 Calculate the cost of 21 notebooks at
9p each.
3 What is the weight of 39 books each weighing 102g?
4 A length of bandage 801 cm long is cut into 9 equal pieces. Find the length of each piece.
5 I pay for 11 items each costing 9p with a £10 note. Find the change I should receive.
6 I buy goods at £11.99, £4.02, £6.03 and £2.98. What is the total bill?
7 399 sweets are divided equally between nine children. How many sweets does each child get and how many are left over?
8 How heavy are 401 books each weighing 2.1 kg?
9 If the diameter of a coin is 2.9 cm, how far would 99 coins stretch if laid end to end?
10 The weight of 11 boxes is 319 g. How much does each box weigh?
11
3.6 x 4.59
9.8
12 12.44 + 8.33
12.54 – 7.22
Upper and Lower Bounds
The real value can be as much as half the
rounded unit above or below the value given. To find the upper bound add on
half the given unit of accuracy, and to find the lower bound subtract half the uniit of accuracy
Example
A length of tubing can only be measured to an accuracy of the nearest metre.
Its measured length is 40 metres. What actual range of lengths could it be?
Upper bound = 40 + ½ of a metre
= 40 + 0.5m
= 40.5 metres
Lower bound = 40 – ½ of a metre
= 40 – 0.5m
= 39.5 metres
Range of values is 39.5 metres to 40 .5 metres
EXERCISE 5
Now calculate the upper and lower bounds of the values given to the accuracy shown.
1 100 grams to nearest gram
2 25 kilograms to nearest kg
3 127 millimetres to nearest mm
4 44 miles to nearest mile
5 1 hour to nearest 10 minutes
6 £3 correct to the nearest pound
7 A parcel weighing 7 kg, correct to the nearest half a kg.