**Convert between decimals and fractions :**

Here we are going to see how to convert decimal to fraction and how to convert fraction to decimal.

**Decimal :**

Decimal number is a number with a decimal point in it, like these:

examples 1.5, 0.6, 3.14,...........

- To convert from decimal to fraction, we have to multiply the given decimal number by 10, 100, 1000 etc accordingly number of digits that we have after the decimal point.
- After multiplying both numerator and denominator by 10, 100, 1000 we have to simplify them.

Let us see some examples based on the above concept.

**Example 1 :**

Convert the following decimal into fraction.

0.75

**Solution :**

**Fraction :**

A fraction simply tells us how many parts of a whole we have. You can recognize a fraction by the slash that is written between the two numbers. We have a top number, the numerator, and a bottom number, the denominator.

We have two ways to represent a fraction as decimal.

- Long division
- Convert the denominator a a multiple of 10, 100, 100 etc.

Let us see some examples to understand how to convert a fraction into decimal.

**Example 2 :**

Convert the following decimal into fraction.

3/5

**Solution :**

Numerator = 3 and denominator = 5

We can convert the denominator as the multiple of 10, 100, 1000 etc.

Here we give some shortcuts to convert the denominator as the multiple of 10, 100, 1000 etc.

**Problem 1 :**

Convert the given fraction into decimal

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, 3/20 = 0.15

**Problem 2 :**

Convert the given decimal into fraction

2.4

**Solution : **

Number digits after the decimal point is 1. So we have to multiply the given decimal value by 10.

2.4 is to be considered as 2.4/1

So, we have to multiply both numerator and denominator by 10.

(2.4/1) x (10/10) = 24/10

We can simplify the numerator and denominator by 2.

= 12/5

Hence the proper fraction equal to the given decimal is 12/5.

**Problem 3 :**

Convert the percentage given below into a proper fraction

0.55

**Solution :**

Number digits after the decimal point is 2. So we have to multiply the given decimal value by 100.

0.55 is to be considered as 0.55/1

So, we have to multiply both numerator and denominator by 100.

(0.55/1) x (100/100) = 55/100

We can simplify the numerator and denominator by 5.

= 11/20

Hence the proper fraction equal to the given decimal is 11/20.

**Problem 4 :**

Convert the given fraction into percentage.

45/8

**Solution :**

We can convert the denominator as the multiple of 10, 100, 1000 etc.

= (45/8) x (125/125)

= 5625/1000

= 0.5625

Hence the decimal equal to the given fraction decimal is 0.5625

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

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