Basic Mathematics Form One Notes – Decimals and Percentages
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Example 1
5.6; 5=wholenumber part and
0.6 = fractional part i.e it can be written as <
é
Therefore 5.6=5£
10
Example 2
() 1335 = 132%
100
a 423
(i) 0123 = 228
1000
(ii) ~~ 208 =2
100
Conversion of Fractions to Terminating Decimals and Vice Versa
Convert fractions to terminating decimals and vice versa
The first place after the decimal point is called tenths. The second place after the decimal point is
called hundredths e.t.c
Consider the decimal number 8.152
The place value of 1 — is tenths (ie =), 5 —is hundredths (ie =) and p –
. ix
is thousandths (ie =.)
F000.
NOTE
. To convert a fraction into decimal, divide the numerator by denominator
+ To convert a decimal into fraction, write the digits after the decimal point as tenths, or
hundredths or thousandths depending on the number of decimal places.
35
Example 3
Conver the following fractions into decimals
1 27 2 37 53
alo Zak Sas
Solution
Divide the numerator by denominator
(a) 0.1
10/1
a.
10
=10 * Z=01
(b) 0.27
10027
=o.
270
=200
700
27
=200 + 2-027
Operations and Decimals
Addition of Decimals
Add decimals
Example 4
Evaluate
36
(a) 28.3+4.96+ 1109
(b) 23.4 + 67.98
Solution
(a) 28.30
4.96
+ 110.90
144.16
(b) 23.40
+ 67.98
91.38
Subtraction of Decimals
Subtract decimals
Example 5
(a) 74-39
(bo) 12.8-17.2
Solution
(a) 74
– 39
3.3
(bo) 120.8
– 172
103.6
37
Multiplication of Decimals
Multiply decimals
Example 6
(a) 23.1 x 67
(b) 4.8 x 67.98
Solution
(a) 23.1% 6.7
231 x 67 = 15477
# 23.1 x 6.7 =154.77
(b) 4.8 x 67.98
48 x 6798 = 326304
+ 48 x 67.98 = 326.304
Mixed Operations with Decimals
Perform mixed operations with decimals
Example 7
(a) 4.5+02
(b) 732+1.28
Solution
97 ts ASE 10 45 _
(a)4.5+0.2=2 =S* 22-225
732 _ 732×100 _ 73200
(b) 732 + 1.28 = 222 = XO _ TR = 571.875
38
Word Problems Involving Decimals
Solve word problems involving decimals
Example 8
If 58 out of 100 students in a school are boys, then write a decimal for the part of the school that
consists of boys.
Solution
We can write a fraction and a decimal for the part of the school that consists of boys.
Fraction decimal
$9100 oss
Percentages
Expressing a Quantity as a Percentage
Express a quantity as a percentage
The percentage of a quantity is found by converting the percentage to a fraction or decimal and
then multiply it by the quantity
Example 9
39
Find (a) 25% of Tsh 60,000
(&) 124 % of 80 cm?
(© 12% of 120 minutes
Solution
a = 25x 60000 _ 15000000 _
(@) 25% of Tsh 60,000 = 3 x 60,000 = == re 7 Tsh 15000
() 122 % of 80cm? = 9 x 80cm? = x 80cm? = BARE = 28 og? =
100 cm?
(© 12% of 120 minutes = 22 x 120 minutes = 22° = TM4 — 1.44 minutes
NOTE:The concept of percentage of a quantity can be used to solve the problems involving
percentage increase and decrease as shown in the below examples:
A Fractions into Percentage and Vice Versa
Convert a fraction into percentage and vice versa
To change a fraction or a decimal into a percentage, multiply it by 100%
Example 10
Convert the following fractions into percentages
40
9
@ |
t
® F
1
(©) 2 F
7
@ |
Solution
@ — = x 100% = 2% = 2 % — 22.5%
40 40 40
a oh = 22109, _ 100 o _ 9 3
) Sx 100% = AH = 2 % = 8.3%
© — 25 100% =F x 100% = =~ Amy — % — 225 %
@ — 2 x 100% = TAM 4 = | = 87.5%
‘A Decimal into Percentage and Vice Versa
Convert a decimal into percentage and vice versa
To change a percentage into a fraction or a decimal, divide it by 100%
Example 11
Convert the following percentages into decimals
a
(a) 662%
(b) 48.5%
(©) 125%
(d) 150%
Solution
1 133 133, _ 133 1 _ 133
(a) 665 % = *%=-—> +100 = 3 Sa bas
oes SES OF
(b) 48.5 % = 705 = z000 = 200
LG of aE ge Bg BO &
SB) BSS Ses St Eten”
_150_ 3
(@ 150% = = 2
Percentages in Daily Life
Apply percentages in daily life
Example 12
In an assignment, Regina scored 9 marks out of 12. Express this asa percentage
Solution
9 out of 12 = 2
out o =
9 9x 100 900
Percentage = 75 x 100 % = 45 — a> %=75%
2
Example 13
{A school has 400 students of which 250 are girls. What percentage of the students are not girls?
_ 250 _ 250 x 100 g, _ 25000 g, _ gn ng
Percentage of girls = ==> x 100 % = 0100 96 — ZR 96 = 62.5%
Percentage which are not girls = 100 % — 62.5 % = 37.5%
3