Converting Between %, Fraction and Decimal
Percentages, fractions, and decimals are three different ways of expressing the same value. 25%, 1/4, and 0.25 all mean the same thing — one-quarter of the whole.
Being able to convert between these three forms is essential for solving problems in maths, science, and everyday life.
What is Converting Between %, Fraction and Decimal - Grade 7 Maths (Comparing Quantities)?
The six conversions:
- % to fraction: Divide by 100, simplify. Example: 75% = 75/100 = 3/4.
- % to decimal: Divide by 100 (move decimal 2 places left). Example: 75% = 0.75.
- Fraction to %: Multiply by 100. Example: 3/4 × 100 = 75%.
- Fraction to decimal: Divide numerator by denominator. Example: 3/4 = 0.75.
- Decimal to %: Multiply by 100. Example: 0.75 × 100 = 75%.
- Decimal to fraction: Write as fraction over power of 10, simplify. Example: 0.75 = 75/100 = 3/4.
Converting Between %, Fraction and Decimal Formula
Quick reference:
% ÷ 100 = Decimal | Decimal × 100 = % | % ÷ 100 = Fraction
Types and Properties
Common equivalents to memorise:
- 10% = 1/10 = 0.1
- 20% = 1/5 = 0.2
- 25% = 1/4 = 0.25
- 33⅓% = 1/3 ≈ 0.333
- 50% = 1/2 = 0.5
- 75% = 3/4 = 0.75
- 100% = 1 = 1.0
Solved Examples
Example 1: Percentage to Fraction
Problem: Convert 60% to a fraction in simplest form.
Solution:
- 60% = 60/100 = 3/5
Answer: 3/5.
Example 2: Fraction to Percentage
Problem: Convert 2/5 to a percentage.
Solution:
- 2/5 × 100 = 200/5 = 40%
Answer: 40%.
Example 3: Decimal to Percentage
Problem: Convert 0.85 to a percentage.
Solution:
- 0.85 × 100 = 85%
Answer: 85%.
Example 4: Percentage to Decimal
Problem: Convert 12.5% to a decimal.
Solution:
- 12.5 ÷ 100 = 0.125
Answer: 0.125.
Real-World Applications
Real-world uses:
- Exams: Marks are given as fractions but reported as percentages.
- Shopping: Discounts (“25% off”) need conversion to decimals for calculation.
- Science: Data in experiments is often recorded as decimals but reported as percentages.
Key Points to Remember
- % to decimal: divide by 100.
- Decimal to %: multiply by 100.
- % to fraction: write over 100 and simplify.
- Fraction to %: multiply by 100.
- Memorise common equivalents (25% = 1/4, 50% = 1/2, etc.).
Practice Problems
- Convert 35% to a fraction in simplest form.
- Convert 7/8 to a percentage.
- Convert 0.06 to a percentage.
- Convert 150% to a decimal.
Frequently Asked Questions
Q1. How do you convert percentage to fraction?
Write the percentage as a fraction over 100 and simplify. For example, 40% = 40/100 = 2/5.
Q2. How do you convert fraction to percentage?
Multiply the fraction by 100. For example, 3/8 × 100 = 37.5%.
Q3. How do you convert decimal to fraction?
Write the decimal as a fraction with the appropriate power of 10 as denominator, then simplify. 0.35 = 35/100 = 7/20.
Related Topics
- Introduction to Percentage
- Converting Fractions to Decimals
- Converting Decimals to Fractions
- Equivalent Fractions
- Percentage Increase and Decrease
- Profit and Loss
- Discount Calculation
- Simple Interest
- Compound Interest
- Applications of Compound Interest
- Sales Tax and VAT
- Growth and Decay
- Finding Percentage of a Number
- Word Problems on Comparing Quantities
