OCR GCSE Maths: Converting Between Fractions, Decimals, and Percentages

Converting Between Fractions, Decimals, and Percentages

This tutorial will guide you through the process of converting between fractions, decimals, and percentages. This is a crucial skill in GCSE Maths and will help you work with all three forms in various mathematical contexts.

Fractions to Decimals

1. Divide the numerator by the denominator:

• Example: Convert 3/4 to a decimal.
• Divide 3 by 4: 3 ÷ 4 = 0.75

2. Terminating vs. Recurring Decimals:

• Terminating decimals have a finite number of digits after the decimal point (e.g., 0.75, 0.5).
• Recurring decimals have a pattern of digits that repeats infinitely (e.g., 1/3 = 0.333...). We indicate repeating digits using a dot over the first and last repeating digit (e.g., 1/6 = 0.1666... = 0.16).

Decimals to Fractions

1. Express the decimal as a fraction with the denominator as a power of ten:

• Example: Convert 0.6 to a fraction.
• 0.6 = 6/10

2. Simplify the fraction to its lowest terms:

• Example: 6/10 simplifies to 3/5.

3. For recurring decimals:

• Example: Convert 0.333... to a fraction.
  • Let x = 0.333...
  • Multiply both sides by 10: 10x = 3.333...
  • Subtract the first equation from the second: 9x = 3
  • Solve for x: x = 3/9 = 1/3

Percentages to Fractions

1. Divide the percentage by 100:

• Example: Convert 25% to a fraction.
• 25% = 25/100

2. Simplify the fraction:

• Example: 25/100 simplifies to 1/4.

Fractions to Percentages

1. Convert the fraction to a decimal (as described above). 2. Multiply the decimal by 100 and add the % sign.

• Example: Convert 2/5 to a percentage.
• 2/5 = 0.4
• 0.4 x 100 = 40%

Decimals to Percentages

1. Multiply the decimal by 100 and add the % sign.

• Example: Convert 0.75 to a percentage.
• 0.75 x 100 = 75%

Practice Problems

1. Convert 1/3 to a decimal.
2. Convert 0.25 to a fraction.
3. Convert 75% to a fraction.
4. Convert 3/4 to a percentage.
5. Convert 0.8 to a percentage.

Remember: Practice makes perfect! The more you practice converting between these forms, the more comfortable you will become with them.