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example 1: Convert the following decimal fractions into decimals.
8 7 673 21 7
(a) (b) (c) (d) 15 (e) 87
10 100 1000 100 1000
Solution: (a) 8 = 0.8 Here is 1 zero in the denominator, so put the
10 decimal point after one digit from the right.

(b) 7 = 0.07 Here are 2 zeros in the denominator, so put the
100 decimal point after two digits from the right.

(c) 673 = 0.673 Here are 3 zeros in the denominator, so put the
1000 decimal point after three digits from the right.

(d) 21 1521
15 = = 15.21 Here are 2 zeros in the denominator, so put the
100 100 decimal point after two digits from the right.

(e) 87 7 = 87007 = 87.007 Here are 3 zeros in the denominator, so put the
1000 1000 decimal point after three digits from the right.

Conversion of Decimals into Fractions

To convert a decimal number into a fraction, take the number without decimal point as
the numerator and in the denominator, write 1 followed by as many zeros as the number
of digits in decimal part.
example 2: Convert the following decimals into fractions.

(a) 0.25 (b) 0.148 (c) 10.5 (d) 2.715

Solution:

(a) 0.25 = 25 0.25 = 25
100 100
1
= 25 = 25 ÷ 25 = (Since HCF of 25 and 100 is 25). 2 decimal 2 zeros
100 100 ÷ 25 4 places
148 148
(b) 0.148 = 0.148 =
1000 1000

148 ÷ 4 37
= = (Since HCF of 148 and 1000 is 4).
1000 ÷ 4 250 3 decimal 3 zeros
places
(c) 10.5 = 105 105
10 10.5 = 10
1
= 105 ÷ 5 = 21 = 10 (Since HCF of 105 and 10 is 5).
10 ÷ 5 2 2 1 decimal 1 zero

(d) 2.715 = 2715 place 2715
1000 2.715 = 1000

= 2715 ÷ 5 = 543 (Since HCF of 2715 and 1000 is 5).
1000 ÷ 5 200 3 decimal 3 zeros
places

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