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

$1.75 = \left ( \frac{1.75}{100} \right) \times 100 = \frac{(1.75 \times 100)}{100} = \frac{175}{100}$

Step 2:

Reducing to lowest terms

$\frac{175}{100} = \frac{7}{4}$

So, 1.75 = $\frac{7}{4}$

Example 2

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

Solution

Step 1:

By definition of a per cent, for any whole number x, x% = $\frac{x}{100}$

Step 2:

To convert the percentage to a fraction, from definition x% = $\frac{x}{100}$.

25% = $\frac{25}{100}$

Reducing to lowest terms

$\frac{25}{100} = \frac{1}{4}$

So, 25% = $\frac{1}{4}$

Example 3

Laura bought a coat in the January sales with $\mathbf{ \frac{1}{5}}$ off the original price. What percentage was taken off the price of the coat?

Solution

Step 1:

The fraction off the original price = $\frac{1}{5}$

Step 2:

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

$\frac{(1 \times 20)}{(5 \times 20)} = \frac{20}{100}$

Step 3:

By definition of percentage

$\frac{20}{100}$ = 20%

So, $\frac{1}{5}$ = 20%