MATHEMATICS - FORM 1
DECIMALS DECIMAL AND FRACTION
1. A decimal is a fraction in which the denominator
is 10 or a power of 10.
For example :-
2. The decimal point ( the dot ) separates
the whole number from its fractional part.
A number written with a decimal point is
known as a decimal.
For example:-
3. The number of digits after the decimal point
is the same as the number of zeros in the
denominator.
For example:-
A) Representing Decimals with Diagrams
Decimals can be represented with diagrams.
For example :-
1 3 9 10 100 1 000
(1 out of 10) (3 out of 100) (7 out of 1 000)
B) Writing Decimals based on given Diagrams
Worked Example Write a decimal to represent the shaded
area in the diagram above.
Solution
The shaded area is3. 10
Therefore, the decimal is 0. 3.
C) Conversion of Fractions into Decimals
and vice versa
1. A fraction in which the denominator is
10 or a power if 10 can be converted to a
decimal mentally.
Worked Example
Express the following as decimals.
(a)7 (c)138 10 1 000(b)52 100
Solution
Worked Example
Change the following into fractions with
denominators of 10 or powers of 10.
(a) 0.6 (b) 0.55 (c) 0.374
Solution
2. A fraction can also be converted to a
decimal by dividing the numerator by
the denominator.
3. Mixed numbers can also be expressed
as decimals.
Worked Example
Express the following fractions as decimals.
(a)3 (b)72 4 5
Solution
Worked ExampleExpress the followingas decimals.
(a)114 (b)45 100 20
Solution
Worked ExampleExpress the following decimals as mixed
numbers.
(a) 3. 6 (b) 11. 025
Solution
(a) 3. 6 = 3 + 0. 6
= 3 +6 10 =36 10
PLACE VALUE AND DIGIT VALUEIN DECIMALS
A) Place Value and Digit Value
1.Eachdigit in a decimal has its own
place value and digit value.
Look at the decimal 8.235 below.
Worked Example
State the place value and digit value
of the underlined digit in each of the
follow decimals.
(a) 13.46 (b) 7.095
Solution
(a) Tenths ; 0.4
(b) Thousandths ; 0.005
2. Decimal places are the number of
places occupied by the digits after
the decimal point.
For example :-
(a) 0.3
1 decimal place
(b) 0.06
2 decimal places
(c) 3.152
3 decimal places
(d) 9.7420
4 decimal places
B) Representing Decimals on Number Lines
A decimal can be represented on a number line.
For example :-
Worked Example
State the decimal represented by each
of the letters on the number line above.
Solution
One part = 4.95 - 4.80
= 0.15
F= 4.95 + 0.15 + 0.15
= 5.25
G= 5.25 + 0.15
= 5.40
Therefore,F= 5.25 andG= 5.40.
C) Comparing Two Decimals
When comparing two decimals, arrange the
digits of the decimals according to their place
values and then compare their digit values
from left to right.
Worked Example
Which is greater, 24.853 or 24.832
Solution
Arrange the decimals as shown below.
At the place value of hundredths, 5 islarger than 3.
Therefore, 24.853 is greater than 24.832.
Worked Example
Fill in each box with ' >' or '
