# Conversion of decimal to fraction

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
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Practice
1) Convert the following decimal to fraction.
a) 0.35
b) 1.75
c) 125.80
d) 0.0105
e) 0.12

Decimals

Expansion of decimals
Comparison of decimals