# Lesson Notes By Weeks and Term - Junior Secondary School 1

APPROXIMATION

SUBJECT: MATHEMATICS

CLASS:  JSS 1

DATE:

TERM: 2nd TERM

REFERENCE BOOKS

• New General Mathematics, Junior Secondary Schools Book 1
• Essential Mathematics for Junior Secondary Schools Book 1

WEEK THREE                                Date: ………………

TOPIC: APPROXIMATION

Content

• Quantitative Reasoning (QR)
• Approximation in our everyday activities

1. Quantitative Reasoning (QR)

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

1. Approximation in Our Everyday Activities

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

1. = 80 and 5. 80 = 6

:. 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

1. = 500km/hr

Average distance in 1hr  = 500km

Evaluation:

1. A farmer has N 200,000 to spend on cattle.  He wants to buy 9 calves.  Each calf costs N18500. Check, by approximation, that the farmer has enough money. Find, accurately how much change he will get after buying the calves.

1. A bucket holds 10.5 litres. A cup holds about 320ml. Estimated the number of cups of water

that the bucket holds.

1.   Essential mathematics
2. New General Mathematics  pg 183 – 186.

Weekend Assignment

1. Find the approximate answer to   0. 41  x 0. 92    (a) 0.6 (b)  0.36 (c ) 0.3 (d) 0.04.
2. Find the rough value of   4 ½   x 1 7/8  (a)  8 (b) 7  (c ) 10 (d) 9
3.   x = 0. 876 – 0.326. By doing a rough calculation, decide which of the following is the value of x

(a) 0.18        (b) 0.21    (c )0.3        (d) 0.55.

1. A cup has a capacity of 290ml. It takes 63 cups to fill a bucket. Find the approximate capacity of the bucket in litres. (a) 9 litres (b) 10 litres (c ) 1800 litres    (d)   18 litres,
2. A sum of N 236000 is divided equally among 54 members of a club.Approximately  how much does each member get? (a) N 4000 (b)N2000    (c) N 20000    (d) N40000.

Theory

1. The table below shows the number of different sizes of shirts sold by a company in a certain month.

Size                Number sold

Small                1243

Medium                4132

Large                3967

Extra large                1985

1. How many shirts were sold altogether?
2. How many more large shirts than small shirts were sold?
3. Check each answer by rounding the numbers to the nearest hundred.

1. Use approximation to find the following
1. 35. 8 – 8.99
2. 7.784  x  97 .5