Master Fractions, Decimals & Percentages Conversion
Corey CrossUnderstanding Fractions, Decimals, and Percentages
Fractions, decimals, and percentages are essential concepts in GCSE and A-Level Maths. They often appear in exams, so mastering their conversions is crucial for success. In this guide, we’ll break down the conversion process with practical examples, tips, and exercises.
What Are Fractions, Decimals, and Percentages?
Before diving into conversions, let’s define these terms:
- Fractions: A fraction represents part of a whole. For example, 1/2 means one part out of two equal parts.
- Decimals: A decimal is another way of expressing parts of a whole, using base-10 notation. For example, 0.5 is equivalent to 1/2.
- Percentages: A percentage expresses parts of a whole as a fraction of 100. For instance, 50% is the same as 1/2 or 0.5.
Converting Between Fractions, Decimals, and Percentages
Fractions to Decimals
To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). For example:
Example: Convert 3/4 to a decimal.
Solution: Divide 3 by 4: 3 ÷ 4 = 0.75. So, 3/4 = 0.75.
Decimals to Fractions
To convert a decimal to a fraction, write the decimal as the numerator and use a power of 10 as the denominator. Then simplify the fraction. For example:
Example: Convert 0.25 to a fraction.
Solution: Write 0.25 as 25/100. Simplify: 25 ÷ 25 / 100 ÷ 25 = 1/4. So, 0.25 = 1/4.
Fractions to Percentages
To convert a fraction to a percentage, multiply it by 100 and add the percentage symbol (%). For example:
Example: Convert 2/5 to a percentage.
Solution: (2 ÷ 5) × 100 = 40%. So, 2/5 = 40%.
Percentages to Fractions
To convert a percentage to a fraction, divide by 100 and simplify. For example:
Example: Convert 75% to a fraction.
Solution: 75 ÷ 100 = 75/100. Simplify: 75 ÷ 25 / 100 ÷ 25 = 3/4. So, 75% = 3/4.
Decimals to Percentages
To convert a decimal to a percentage, multiply it by 100 and add the percentage symbol (%). For example:
Example: Convert 0.6 to a percentage.
Solution: 0.6 × 100 = 60%. So, 0.6 = 60%.
Percentages to Decimals
To convert a percentage to a decimal, divide by 100. For example:
Example: Convert 20% to a decimal.
Solution: 20 ÷ 100 = 0.2. So, 20% = 0.2.
Common Conversions Table
Here’s a handy table for common conversions:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
Practice Exercises
Test your understanding with these exercises:
- Convert 5/8 to a decimal.
- Convert 0.125 to a fraction.
- Convert 40% to a decimal.
- Convert 0.75 to a percentage.
Check your answers at the end of this page! [LINK:/lessons]
Exam Technique Tips
Here are some essential tips to tackle fractions, decimals, and percentages in exams:
- Show your working: Even if your final answer is incorrect, showing your steps can earn marks.
- Memorise common conversions: Knowing common fractions and their decimal or percentage equivalents can save time.
- Use a calculator: For GCSE exams, use the calculator effectively to avoid manual errors.
- Check your answers: Always verify your answers by reversing the conversion.
"By practising conversions regularly, you’ll gain confidence and speed in dealing with fractions, decimals, and percentages."
Need more help? Explore interactive lessons with our AI tutors [LINK:/genies]!