**Introduction: **

## Relation between fraction, decimal and percent:

Since a percent is a ratio that can be written as a fraction, and a fraction can be written as a decimal. This means any of these forms can be converted to any of the others.

**To Convert a Fraction:**

**To a decimal: **Divide the numerator by the denominator.

**To a percent: **Convert the fraction first to a decimal, then move the decimal point 2 places to the right and add the % symbol.

**To Convert a Decimal:**

**To a fraction: **Read the decimal and reduce the resulting fraction.

**To a percent: **Move the decimal point 2 places to the right and add the % symbol.

**To Convert a Percent**

**To a decimal: **Move the decimal point 2 places to the left and drop the % symbol.

**To a fraction:** Drop the % sign and write the number “over” 100. Reduce, if possible.

Let’s understand the above conversion by examples

**Example3** Convert ¾ in decimal form.

**Example4 **Convert 3/8 in decimal form.

Observe the images given below and find the similarity.

**Image1:-**

Here in the above picture shaded block can be represented in three ways:

- Fraction – 30/100 or 3/10

- Decimal – 0.3 = 0.30

- Percent – 30%

**Image2:-**

Here all three jugs represent the half quantity of liquid of whole you can write them in any of the way like:

- 50%

- ½

- 0.5

**Fraction into Percent:**

**Example1 **Convert 60/100 as a percent:

**Example2 **Observe the image and convert the fraction in the percent.

**More Word Problems: Understand Percent**

**Question1: –** Teddy spend 3/8 of his homework time doing Math problems. Write 3/8 as a decimal and as a percent.

**Solution: **

= 0. 375

Therefore, 3/8 = 0.375

**Use the decimal to find the equivalent rate:**

0.375 =

** =**37.5%

**Question2: –** Convert

178178

to a decimal and a percent.

**Solution: **Write the mixed fraction as 1 +

7878

**Decimal:**

= 1 + 0.875

= 1.875

**Percent:**

1.875 = (1.875** ****× ****100)%**

= 187.5%

Note: To convert the decimal number into percent

we can directly multiply it with 100 and follow it with a

a % sign.

**Concept Map:**

In each diagram, the same area is shaded

But it’s not easy to see that the Fraction, the Decimal and the Percentage all have the same value, because the Fraction and the Decimal have been simplified

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