# Conversion of decimal to fraction

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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
Subtraction of Decimals
Multiplication of Decimals
Division of Decimals
Conversion of decimal to fraction

From conversion of decimals to Introduction of decimals

Number System