**Equivalent Fractions and Decimals :**

Fractions and decimals that represent the same value are equivalent.

For example, 1//4 and 0.25 are equivalent.

Because,

1/4 = 0.25

The number line shows some equivalent fractions and decimals from 0 to 1.

To get the decimal equivalent to the fraction given, first we have to check whether the denominator of the fraction is convertible to 10 or 100 using multiplication.

**Method 1 : **

If it is convertible to 10 or 100 using multiplication, we can convert the given fraction into decimal as explained below.

**Method 2 : **

If it is not convertible to 10 or 100 using multiplication, we can get the decimal equivalent to the given fraction as explained below.

To get fraction equivalent to the given decimal, first we have to count the number of digits after the decimal.

(i) If there is only one digit after the decimal, we have to multiply and divide the decimal number by 10.

**Example :**

0.2 = (0.2 ⋅ 10)/10

0.2 = 2/10

0.2 = 1/5

Therefore, the fraction equivalent to the decimal 0.2 is 1/5

(ii) If there are two digits after the decimal, we have to multiply and divide the decimal number by 100.

**Example : **

0.25 = (0.25 ⋅ 100)/100

0.25 = 25/100

0.25 = 1/4

Therefore, the fraction equivalent to the decimal 0.25 is 1/4

**Note :**

If there are three digits after the decimal, we have to take 1000 as denominator and so on.

**Problem 1 : **

Look at the number line given below and write the missing decimals and fractions.

**Solution :**

**Problem 2 :**

Find the decimal equivalent to the fraction given below.

3/20

**Solution : **

In the given fraction, the denominator is 20 which is convertible to 100 using multiplication by 5.

So, we have

3/20 = (3x5)/(20x5) = 15/100 = 0.15

Hence, the decimal equivalent to the fraction 3/20 is 0.15

**Problem 3 :**

Find the decimal equivalent to the fraction given below.

7/10

**Solution : **

In the given fraction, the denominator is 10.

So, we have

7/10 = 0.7

Hence, the decimal equivalent to the fraction 7/10 is 0.7

**Problem 4 :**

Find the fraction equivalent to the decimal given below.

0.85

**Solution : **

In the given decimal, there are two digits after the decimal.

So, we can write the given decimal as fraction with denominator 100.

That is,

0.85 = 85/100

0.85 = 17/20

Hence, the fraction equivalent to the decimal 0.85 is 17/20.

**Problem 5 :**

Find the fraction equivalent to the decimal given below.

0.305

**Solution : **

In the given decimal, there are three digits after the decimal.

So, we can write the given decimal as fraction with denominator 1000.

That is,

0.305 = 305/1000

0.305 = 61/200

Hence, the fraction equivalent to the decimal 0.305 is 61/200.

After having gone through the stuff given above, we hope that the students would have understood equivalent fractions and decimals.

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