# Converting Between Percentages and Decimals in a Real-World Situation

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

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 = $\frac{7}{4}$

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% = $\frac{x}{100}$**

**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% = $\frac{1}{4}$

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%