For conversion of decimal to fraction, follow the following steps.
Step 1: Put 1 in the denominator $\frac{2.6}{1}$
Step 2: Shift the decimal to right place $\frac{2.6}{1}=\frac{2.6}{10}$ (1 shift)
Step 3: Count the shifts and put that much zeros with 1, $\frac{26}{10}$
Step 4: Convert the fraction in lowest (reduced form )if possible.
$\frac{26\div 2}{10\div 2}=\frac{13}{5}$
Example 1: Express 1.28 in fraction
1.28 = $\frac{1.28}{100}$ (shifting of decimals by 2 places)
= $\frac{128\div 2}{100\div 2} = \frac{64}{50}$
= $\frac{64\div 2}{50\div 2}$
= $\frac{32}{25}$
Example 2: Express 0.777 in fraction
0.777 = $\frac{0.777}{1000}$ (shifting of decimals by 3 places)
= $\frac{777}{1000} $
Some more examples
1) Convert 34.178 into a fraction.
Solution :
Decimal fraction = 34.178
Decimal places = 3
Thus, Numerator = 34178 x 1000
Denominator = 1000
Fraction = 34178 /1000
= 34178/1000 ÷ 2/2
= 17089/500
2) Convert 0.76 into a fraction.
Solution :
76/100
= 76/100 ÷ 2/2
= 38/50
3) Convert 1.8 into a fraction.
Solution :
18/10
= 18/10 ÷ 2/2
= 9/5
4) Convert 0.25 into a fraction.
Solution :
25/100
= 25/100 ÷ 5/5
= 5/20 ÷ 5/5
= 1/4
5) Convert 1225.8 into a fraction.
Solution :
12258/10
= 12258/10 ÷ 2/2
= 6129/5
6) Convert 0.80 into a fraction.
Solution :
80/100
= 80/100 ÷ 10/10
= 8/10 ÷ 2/2
= 4/5
7) Convert 0.66 into a fraction.
Solution :
66/100
= 66/100 ÷ 2/2
= 33/50
8) Convert 0.025 into a fraction.
Solution :
25/1000
= 25/1000 ÷ 5/5
= 5/200 ÷ 5/5
= 1/40
9) Convert 4.25 into a fraction.
Solution :
425/100
= 425/100 ÷ 5/5
= 85/20 ÷ 5/5
= 17/4
10) Convert 15.05 into a fraction.
Solution :
1505/100
= 1505/100 ÷ 5/5
= 301/20
11) Convert 0.008 into a fraction.
Solution :
8/1000
= 8/1000 ÷ 8/8
= 1/250
________________________________________________________________________ Practice
1) Convert the following decimal to fraction.
a) 0.35
b) 1.75
c) 125.80
d) 0.0105
e) 0.12 Decimals
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