# 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

• Addition of Decimals

• Subtraction of Decimals

• Multiplication of Decimals

• Division of Decimals

• Conversion of decimal to fraction

Number System

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