The Trio of Numerical Expression: Fractions, Decimals, and Percentages

Imagine you have a delicious pizza divided into 4 equal parts and you eat 1 slice. You could say you ate $\frac{1}{4}$ of the pizza (fraction), or 0.25 of the pizza (decimal), or even 25% of it (percentage). These three ways of expressing quantities are interconnected, each offering a unique perspective on the part of a whole you enjoyed. 

 

Understanding Fractions, Decimals, and Percentages

• Fraction: Shows part of a whole, like $\frac{1}{2}$, where the top number (numerator) tells how many parts you have, and the bottom number (denominator) shows how many equal parts make up the whole.
• Decimal: Shows part of a whole as a number after a decimal point, like $0.5$
• Percentage: A fraction out of 100, often written with a "$\%$" symbol like $50\%$

 

How to Convert between Fractions, Decimals, and Percentages

Converting Fractions to Decimals

To convert a fraction to a decimal:

1. Divide the numerator by the denominator.

Example

Convert $\frac{3}{4}$ to a decimal. $$\frac{3}{4} = 3 \div 4 = 0.75$$

So, $\frac{3}{4}$ as a decimal is $0.75$

 

Converting Decimals to Fractions

To convert a decimal to a fraction:

1. Write down the decimal as a fraction with $10, 100, 1000$, etc., in the denominator, depending on the number of decimal places.
2. Simplify the fraction if needed.

Example

Convert $0.75$ to a fraction. $$0.75 = \frac{75}{100} = \frac{3}{4} \quad \text{(after simplifying)}$$

So, $0.75$ as a fraction is $\frac{3}{4}$

 

Converting Fractions to Percentages

To convert a fraction to a percentage:

1. Divide the numerator by the denominator.
2. Multiply the result by $100\%$

Example

Convert $\frac{3}{4}$ to a percentage. $$\frac{3}{4} = 0.75 \times 100\% = 75\%$$

So, $\frac{3}{4}$ as a percentage is $75\%$

 

Converting Percentages to Fractions

To convert a percentage to a fraction:

1. Write the percentage as a fraction with $100$ as the denominator
2. Simplify the fraction if possible.

Example

Convert $75\%$ to a fraction. $$75\% = \frac{75}{100} = \frac{3}{4} \quad \text{(after simplifying)}$$

So, $75\%$ as a fraction is $\frac{3}{4}$.

 

Converting Decimals to Percentages

To convert a decimal to a percentage:

1. Multiply the decimal by $100\%$

Example

Convert $0.75$ to a percentage. $$0.75 \times 100\% = 75\%$$

So, $0.75$ as a percentage $75\%$

 

Converting Percentages to Decimals

To convert a percentage to a decimal:

1. Divide the percentage by $100$

Example

Convert $75\%$ to a decimal. $$75\% \div 100 = 0.75$$

So, $75\%$ as a decimal is $0.75$