SUBJECT: MATHEMATICS
CLASS: JSS 1
DATE:
TERM: 2nd TERM
REFERENCE BOOKS
WEEK THREE Date: ………………
TOPIC: APPROXIMATION
Content
Example
Calculate the value of the following and give your answer correct to the number of significant figures stated:
(a) 46 x 34 correct to 2.f.
(b) 346 x 24 correct to 3 s.f
(c )5.766 + 81.34 correct to 1 s.f
(d) 72.63 – 8.35 correct to 3 s.f
Solution
(a) 46 x 34 (c ) 5.766 + 81. 34
4 6 5. 7 66
x 3 6 + 81. 35
1 8 4 87.106
+1 3 8 :. 87. 106 = 90 to 1 s.f
1 5 6 4
1564 = 1600 ( to 2 s.f)
(b) 3 4 6 x 24 (d ) 72.63 – 8.23
3 4 6 7 2 . 6 3
x 2 4 - 8. 3 5
1 3 8 4 6 4. 2 8
+ 6 9 2
8 3 0 4 :. 64.28 = 64.3( to 3 s.f)
8304 = 8300 ( 3.s.f)
Evaluation:
Evaluate the following and give your answers correct to two significant figures.
(a) 0. 46 x 0. 35
20
(b) 12.3 x 32.0
16
(c) 0.052 + 0.045
4
(d ) 3. 07 + 0. 97
5
Approximation is a way of using rounded numbers to estimate answers to a calculation. Approximation can help us decide whether an answer to a calculation is of right size or not. To find an approximate answer to a calculation, round the numbers to easy numbers, usually 1 s.f., or 2.s.f. or to the nearest whole number. Then work out the approximated answer using these easy numbers.
Example 1
A boy was asked to calculate the cost of 82 oranges at N 5.80 each
Solution
Rough calculation
:. Approximated cost = 80 x 6
= N 480.
Actual calculation
82 x 5. 80
= N 475. 60
comparing the rough calculation with the actual calculation, you will discover that the two answers
N 480 and N 475.60 are very close.
Example 2
A box full of exercise books weighs 12kg. if one exercise book weighs 10.2g.find the approximate number of exercise books in the box.
Solution
By approximate answer, we mean the rough calculation.
Weight ( total ) = 12kg
12kg = 10kg
one exercise book = 10.2g
10.2g = 10g
approximate number of exercise books.
= 10kg
10g
but, 1000g = 1kg
= 10 x 1000g
10 g
= 1000 books
Example 3
In 2008 the value of a plot of land was N 238000. Its value rises by about 110% each year. Estimate its value in2009 to the nearest N 1000.
Solution
In 2008,
Cost = N238000
Rise = 10%
= 10 x 238000
100
N23800
Value in 2009,
= N 238000
N 23800
N 261800
. N 261800 = N262000
Example 4
The population of five towns are 15600, 17300,62800, 74000 and 34400, each to the nearest hundred. Find the total population of the 5 towns to the nearest thousand.
Solution
Total population of the 5 towns
1 5 6 0 0
1 7 3 0 0
6 2 8 0 0
7 4 0 0 0
3 4 4 0 0
2 0 4 1 0 0
= 204100 = 204000 ( to the nearest thousand)
Example 5
An aeroplane flies 2783km in 5 ¾ hours. First approximate, then calculate the average distance it flies in 1 hour.
Solution
Distance = 2783km
2783km = 3000km
time = 5 ¾ hours
5 ¾ = 6 hours
Approximate distance = 3000km
Approximate time = 6 hours
Average speed = 3000
Average distance in 1hr = 500km
Evaluation:
that the bucket holds.
Reading Assignment
Read about Base Numbers.
Weekend Assignment
(a) 0.18 (b) 0.21 (c )0.3 (d) 0.55.
Theory
Size Number sold
Small 1243
Medium 4132
Large 3967
Extra large 1985
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