ESTIMATION
Estimation comes in two forms. In both cases you are estimating to see if your answer is a
sensible one.
Estimating a quantity
 Some times you need to roughly guess, or estimate, the size of a quantity, be it in
kilograms, litres or metres. For example:
 The weight of a new born baby
 The fuel consumption of a car
 The capacity of a bucket
 The diameter of a car tyre
 The width of a road
 When estimating such quantities it is advisable to use a comparison with something that
you are familiar with. For example:
 The height of a door - use the height of a man and add enough to give plenty
headroom.
 The capacity of a bucket - how many litre bottles of Coke could you put in it?
 The weight of a new born baby – what comparison is there with a kilogram of
apples or some other item that you buy regularly?
Estimation for a calculation
 When performing a calculation, you need to be able to estimate the expected answer.
 When going shopping you might want to work out if you have enough money to pay
for the items you wish to purchase.
 When doing a calculation you need to be sure that your answer is of the right size.
Even if you use a calculator you might strike a wrong key and multiply instead of
divide.
 When estimating in this way you need to simplify the calculation to make it easier to
work out.
 You need to round the figures in the calculation to simpler numbers that you can work
with easily. Namely you round the numbers in the calculation.
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Updated Feb 2013
 When you round a number, you round down if the following number is between 1 and 4,
and round up if the following number is between 5 and 9. For example:
 2456 would be 2500 to the nearest hundred
2456 is nearer to 2500 than to 2400
 2456 would be 2000 to the nearest thousand
2456 is nearer to 2000 than to 3000
 49.5 would be 50 to the nearest ten
49.5 is nearer to 50 than to 40
 0.045 would be 0.05 to the nearest hundredth
 The following are examples of estimates of calculations made easier by rounding the
numbers.
 57  $18.99
simplify to 60  $20  $1200
 $4.50 + $ 27.90 + $52.10 + $199.99 + $31.25
simplify to $5 + $30 + $50 + $200 + $30  $315

28.6  99.1 4.7
30 100  5

 3
532.1 8.9
500 10
(actual answer is 2.81)
This gives an idea of the relative size of answer to expect. If you were asked in a
multiple choice question which of the following gives the closest answer:
( 0.03,
0.3,
3,
30,
300,
3000)
you would know to choose 3.
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Estimation Exercises
1. For the following, estimate the answer then find the exact answer:
a) The price of a used car on hire purchase is $6864 including interest. If the
repayments are $33 per week, how many weeks would it take to pay the car off?
b) A stereo can be bought on hire purchase for $8 per week over 3 years. What will
be the total cost?
c)
If Tom earns $ 595 per week, how much does he earn per year?
d) A car's petrol consumption averages 12 litres per 100 km.
i) How many litres would be used to travel 700 km?
ii) If petrol costs 101 cents per litre, what is the total cost of
the petrol?
e) A human heart beats on average 70 times per minute.
i) How many times does it beat per day?
ii) How many times does it beat per year?
f) A landlord receives $95 680 per year rent for a block of flats. There are 8 flats in
the block, how much is the weekly rent for each flat?
g) Paul has two part time jobs. Job One pays him $12 per hour for 16 hours per
week. Job Two pays him $15 per hour for 24 hours per week. What is his total
income per week?
h) If there are 350 people in a theatre and each person paid $18 for a ticket, how
much money was collected in total?
i)
What is the yearly wage bill for a company with 39 employees, earning an average
of $22 500 per annum?
j)
On average, each day 285 000 copies of a particular newspaper are sold.
i)
How many papers is this per week?
ii)
How many per year?
k) The area of Australia is 7 682 000 square kilometres. The area of the United
Kingdom is 244 000 square kilometres. How many times greater is Australia than
the United Kingdom?
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2. For the following, choose the value closest to the solution of the calculation:
a)
19.4  4.3
b)
4.68  29.4  50.3
c)
65.3  9.99
79.5
(0.01
d)
0.53 124
415
e)
(0.8
8
80
800)
7500
75 000)
0.1
1
10)
(0.01
0.1
10
100)
754 2.75
34.3
(0.5
5
50
500)
f)
2.346  19.35
723
(0.05
0.5
5
50)
g)
49.4  24.5
6.81 4.7
( 0.3
10
40
300)
h)
28.3  720.1
89.33  61.4
(0.4
4
40
400)
i)
793.1 495.3
98.6  4.2
(1
100
1000
10 000)
j)
192.5  63.2
5940.2  22.1
(0.009
0.09
k)
29.2  7.7
0.029  0.42
(2
(75
750
200
2000
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0.9
9
20 000
90)
200 000)
Estimation exercises solutions
1. a) 7000  30  200
208 weeks
b) 10  3  50 = $1500
c)
$1248
600  50 = $30 000
$30 940
7  10 = 70
84 litres
d) i)
ii) 100  80 = 8000 cents = $80
$84.84
i) 70  60  20 = 84 000
100 800 times
ii) 80 000  400 = 32 000 000
36 792 000 times
f)
100 000  10  50 = $200
$230
g)
(10  20) + (20  20) = 600
$552
e)
h) 400  20 = 8000
$6300
i)
40  20 000 = $800 000
$877 500
j)
i) 300 000  7 = 2 100 000
1 995 000
ii) 300 000  400 = 120 000 000
104 025 000
8 000 000  200 000 = 40
31.5 times
k)
2. a) 80
b) 7500
c)
10
d) 0.1
e) 50
f)
0.05
g) 40
h) 4
i)
1000
j)
0.09
k)
20 000
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Updated Feb 2013