Converting Between Percentages and Decimals in a Real-World Situation

Introduction

In this lesson, we are solving real world problems related to conversion between percentages and decimals.Example 1

Lizzy bought some fabric that was 1.75 meters long. How could this be written as a fraction?

Solution

Step 1:

To convert the decimal to a fraction we multiply and divide by 100

1.75=(1.75100)×100=(1.75×100)100=1751001.75=(1.75100)×100=(1.75×100)100=175100

Step 2:

Reducing to lowest terms

175100=74175100=74

So, 1.75 = 7474Example 2

Kylie pays tax at the rate of 25% of her income. What fraction of Kylie’s income is this?

Solution

Step 1:

By definition of a per cent, for any whole number x, x% = x100�100

Step 2:

To convert the percentage to a fraction, from definition x% = x100�100.

25% = 2510025100

Reducing to lowest terms

25100=1425100=14

So, 25% = 1414Example 3

Laura bought a coat in the January sales with 1515 off the original price. What percentage was taken off the price of the coat?

Solution

Step 1:

The fraction off the original price = 1515

Step 2:

To convert the fraction to percentage, multiply and divide it by 20

(1×20)(5×20)=20100(1×20)(5×20)=20100

Step 3:

By definition of percentage

2010020100 = 20%

So, 1515 = 20%