Page 159 - Start Up Mathematics_6

Representation of Decimals on a Number Line
In our previous lesson, we represented fractions on a number line. Now let’s learn to represent
decimals on a number line.
Let’s represent 0.7, 1.5 and 2.3 on a number line. Since, 0.7, 1.5 and 2.3 lies between 0 and 3,
divide each unit in the interval 0 to 3 into 10 equal parts and represent the decimals as shown.

0 0.7 1 1.5 2 2.3 3

Converting a Fraction into a Decimal

A fraction with denominator 10 or its higher power can be converted to decimals easily. Therefore,
it is convenient to find the decimal equivalent of a fraction by converting its denominator into
some power of 10. In order to convert a fraction into a decimal, we follow these steps:
Step 1: Obtain the fraction and convert it into an equivalent fraction with denominator 10; 100
or 1,000, ... etc.
Step 2: Write the numerator and mark decimal point after as many places from the right as there
are zeros after one in the denominator.
168 7
For example, = 1.68 = 0.007
100 1,000
3 3 × 25 75 13 13 × 2 26
= = = 0.75 = = = 2.6
4 4 × 25 100 5 5 × 2 10

Converting a Decimal into a Fraction
In order to convert a decimal into a fraction, we follow these steps:

Step 1: Obtain the decimal number.
Step 2: Write the numerator as the number obtained by removing the decimal.
Step 3: Write the denominator as 1 followed by as many zeros as there are decimal places in
the number.
5 1 13 125 1
For example, 0.5 = = , 1.3 = , 0.125 = =
10 2 10 1,000 8
Example 1: Write the following as numbers using the place value table.

(a) (b)

Tens Ones Tenths Hundreds Tens Tenths
Solution: 1
Hundreds (100) Tens (10) Ones (1) Tenths Number
10
(a) 0 2 3 2 23.2
(b) 1 2 0 5 120.5

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