Name of Lecturer: Mr. J.Agius
Course: FCES
LESSON 24
Percentages and their Applications
Approximations
24.1 Rounding Whole Numbers
We have seen that it is sometimes unnecessary and often impossible to give exact values. In
the case of measurements this is particularly true. However, we do need to know the degree
of accuracy of an answer. For example, if a manufacturer is asked to make screws that are
about 12½ cm long, he does not know what is acceptable as being “about 12½ cm long”! But
if he is asked to make them 12.5cm long correct to one decimal place, he knows what
tolerances to work to.
Whole numbers are divided into units, tens, hundreds, thousands, etc. When we are told to
approximate to the nearest 10 we look at the units. If there are 5 or more units you add one to
the tens. If there are less than 5 units you leave the tens alone.
Similar rules apply to rounding off to the nearest 100 (look at the tens); to the nearest 1000
(look at the hundreds); and so on.
Example 24A
The attendance at a pop concert was 12134, the exact number of tickets sold.
12134 can be rounded to the nearest ten, hundred, thousand, and so on …
To the nearest ten:
To the nearest hundred:
To the nearest thousand
1213│4
121│34
12│134
12130
12100
12000
To the nearest hundred in general can be used for catering.
To the nearest thousand in general can be used by newspaper reporter.
Example 24B
Round the measurement 555mm:
a)
b)
to the nearest 10mm
to the nearest 100mm
555mm is exactly halfway between 550mm and 560mm. When rounding to the nearest
10mm, 555mm rounds upwards to become 560mm.
555mm is between 500mm and 600mm, but nearer 600mm. When rounding to the nearest
100mm, 555mm becomes 600mm.
Learning Outcome 1 – Numerical Calculations
Page 120
Name of Lecturer: Mr. J.Agius
Course: FCES
Exercise 24A
1.
Round off each of the following value to
Nearest ten
i)
2479
ii)
56741
iii)
€31 297
iv)
11 362m
a)
b)
c)
the nearest ten
the nearest hundred
the nearest thousand
Nearest Hundred
Nearest thousand
2.
The attendance at an athletics meeting was 12 937.
Write this figure to the nearest 100.
3.
During the summer season the number of visitors to a heritage centre was 18894.
Write this figure to the nearest 1000.
4.
The estimated cost of a school extension is £24 980. Write this estimate to the nearest
£1000.
5.
Give an approximate answer for each number below.
a)
James has a flock of 142 chickens.
b)
Mrs Wilson sold 306 portions of fish and chips.
c)
Asif needed 6318 bricks to build his new bungalow.
d)
A crowd of 35157 spectators watched Chelsea last night.
e)
A pop group earned £45 376 290 in a year.
Learning Outcome 1 – Numerical Calculations
Page 121
Name of Lecturer: Mr. J.Agius
Course: FCES
6.
Liners
Launched
Length
Tonnage
Speed
Queen Elizabeth
Queen Mary
New P&O cruise
liner
QE2
United States
Canberra
1938
1934
1,029 ft
1,019 ft
83,673
80,774
32 knots
32 knots
(1994-5)
850 ft
67,000
24 knots
1967
1951
1960
963 ft
990 ft
820 ft
65,863
53,329
45,270
32.5 knots
40 knots
29.3 knots
Tonnage
Speed
For each of these liners, round:
a)
the lengths to the nearest ten feet
b)
the tonnages to the nearest hundred tonnes
c)
the speeds to the nearest ten knots.
Liners
Launched
Length
Queen Elizabeth
Queen Mary
New P&O cruise
liner
QE2
United States
Canberra
7.
The table gives the areas and populations of five European Union states.
Country
Area (km2)
Population
Greece
Italy
Netherlands
Germany
Ireland
131 944
301 225
33 812
356 733
70 283
9 804 266
57 436 280
14 292 416
80 180 660
3 521 000
Round:
a)
The areas to the nearest thousand km2.
b)
The populations to the nearest hundred thousand.
Country
Area (km2)
Population
Greece
Italy
Netherlands
Germany
Ireland
Learning Outcome 1 – Numerical Calculations
Page 122
Name of Lecturer: Mr. J.Agius
Course: FCES
24.2 Rounding to a Number of Decimal Places
There are times when you work sometimes out on your calculator and the number fills the
whole display. The answer is far more accurate than you need. Instead of using all the digits
you can round the number to a given number of decimal places.
To correct 0.07822 to two decimal places (d.p) we look at the third decimal place. If it is 5 or
larger, we add 1 to the figure in the second decimal place. If it is less than 5, we do not alter
the figure in the second decimal place.
Example 24C
Find 0.07822 correct to
a)
b)
c)
3 d.p.
2.d.p.
1d.p.
Answer
a)
b)
c)
0.078|22 = 0.078
0.07|822 = 0.08
0.0|7822 = 0.1
correct to 3 d.p.
correct to 2 d.p.
correct to 1 d.p.
Note; We begin to count decimal places from the decimal point and the answer should have
the same number of decimal places you are correcting for.
All the numbers after that decimal point are converted to zero automatically.
Exercise 24C
Round off each of the following values correct to
a)
b)
c)
1)
0.2749
Ans. a)________
Ans. b)________
Ans. c)________
2)
1.4263
Ans. a)________
Ans. b)________
Ans. c)________
3)
0.0457
Ans. a)________
Ans. b)________
Ans. c)________
4)
5.6616
Ans. a)________
Ans. b)________
Ans. c)________
Learning Outcome 1 – Numerical Calculations
3 d.p.
2 d.p.
1d.p.
Page 123
Name of Lecturer: Mr. J.Agius
Course: FCES
Mixed Exercises
1) The value of  is 3.141592… Write this value correct to
a) 1 decimal place
2)
b) 2 decimal places
c) 3 decimal places
Use your calculator to find the square root of 20.
Write this value correct to
a) 1 decimal place
b) 2 decimal places
c) 3 decimal places
3) How many decimal places do you give if your answer is correct to the nearest
a) tenth?
4)
b) hundredth?
For each of these, write down your estimate of the reading to the nearest hundredth, and
then write the reading correct to the nearest tenth.
a)
b)
5
8
6
9
5) Write these fractions as decimals correct to 3 decimal places.
a)
b)
c)
d)
6) Calculate 12.6% of 43.8, giving your answer correct to 2 decimal places.
Measure the length and width of this rectangle in centimetres giving your answer
correct to 1 decimal place.
7) a)
b)
Use these values to calculate the area of the rectangle giving your answer correct to
1 decimal place.
Work out the mean of these numbers giving your answer correct to 2 decimal places.
8)
4, 4, 5, 7, 8, 12, 15
9) A circle has radius 7.3m. Using  = 3.14 calculate, correct to 1 decimal place,
a) Its circumference
Learning Outcome 1 – Numerical Calculations
b) Its area.
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