Converting between Fractions, Decimals and Percentages

Understanding how to convert between fractions, decimals, and percentages is a key skill in GCSE Maths. This guide will cover the steps and methods required to perform these conversions, with examples to help you practice and understand the processes.

Converting Decimals to Fractions and Percentages

Decimals to Fractions

To convert a decimal to a fraction, follow these steps:

1. Write the decimal as a fraction:
   • If the decimal has one decimal place (e.g., 0.5), place it over 10 (i.e., $\frac{5}{10}$​).
   • If the decimal has two decimal places (e.g., 0.75), place it over 100 (i.e., $\frac{75}{100}$​).
2. Simplify the fraction:
   • Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).

Example 1: Convert 0.4 to a fraction.

• Write 0.4 as $\frac{4}{10}$​.
• Simplify the fraction: divide both the numerator and denominator by 2 to get $\frac{2}{5}$​.

Example 2: Convert 0.6 to a fraction.

• Write 0.6 as $\frac{6}{10}$​.
• Simplify the fraction: divide both the numerator and denominator by 2 to get $\frac{3}{5}$​.

Decimals to Percentages

To convert a decimal to a percentage, simply multiply the decimal by 100 and add the percentage symbol (%).

Example 1: Convert 0.5 to a percentage.

• Multiply 0.5 by 100: $0.5\times 100 = 50$.
• The answer is 50%.

Example 2: Convert 0.75 to a percentage.

• Multiply 0.75 by 100: $0.75\times 100 = 75$.
• The answer is 75%.

Converting Fractions to Decimals and Percentages

Fractions to Decimals

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number).

Example 1: Convert $\frac{3}{4}$​ to a decimal.

• Divide 3 by 4: $3\div 4 = 0.75$.
• The answer is 0.75.

Example 2: Convert $\frac{7}{8}$​ to a decimal.

• Divide 7 by 8: $7\div 8 = 0.875$.
• The answer is 0.875.

Fractions to Percentages

To convert a fraction to a percentage:

1. Convert the fraction to a decimal (as shown above).
2. Multiply the decimal by 100 to get the percentage.

Example 1: Convert $\frac{1}{2}$ to a percentage.

• Convert $\frac{1}{2}$​ to decimal: $1\div 2 = 0.5$.
• Multiply 0.5 by 100: $0.5\times 100 = 50$.
• The answer is 50%.

Example 2: Convert $\frac{3}{5}$​ to a percentage.

• Convert $\frac{3}{5}$​ to decimal: $3 \div 5 = 0.6$.
• Multiply 0.6 by 100: $0.6\times 100 = 60$.
• The answer is 60%.

Converting Percentages to Decimals and Fractions

Percentages to Decimals

To convert a percentage to a decimal, divide the percentage by 100 or simply move the decimal point two places to the left.

Example 1: Convert 45% to a decimal.

• Divide 45 by 100: $45 \div 100 = 0.45$.
• The answer is 0.45.

Example 2: Convert 0.25% to a decimal.

• Divide 0.25 by 100: $0.25\div 100 = 0.0025$.
• The answer is 0.0025.

Percentages to Fractions

To convert a percentage to a fraction:

1. Write the percentage as a fraction over 100.
2. Simplify the fraction, if possible.

Example 1: Convert 60% to a fraction.

• Write 60% as $\frac{60}{100}$​.
• Simplify by dividing both the numerator and denominator by 20: $\frac{60}{100} = \frac{3}{5}$​.
• The answer is $\frac{3}{5}$​.

Example 2: Convert 25% to a fraction.

• Write 25% as $\frac{25}{100}$​.
• Simplify by dividing both the numerator and denominator by $\frac{25}{100} = \frac{1}{4}$​.
• The answer is $\frac{1}{4}$​.

Summary of Conversion Methods

By mastering these conversions, you will be able to confidently tackle questions involving fractions, decimals, and percentages in your GCSE Maths exams.