Conversions Involving Percentages, Fractions And Decimals
Fractions, decimals, and percentages are three different ways of representing the same value. Understanding how to convert between them is essential for solving problems in measurement, estimation, comparison, and real-life applications like discounts, interest rates, and data interpretation.
Converting Decimals to Fractions
To convert a decimal to a fraction, follow these steps:
- Write the decimal as a fraction with denominator 1
- Multiply both numerator and denominator by 10 for each digit after the decimal point
- Simplify the fraction by dividing by the highest common factor (HCF)
Example 1: Convert 0.75 to a fraction
0.75 has 2 decimal places → multiply by 100
0.75 = ⁷⁵⁄₁₀₀
Simplify: divide numerator and denominator by 25
Answer: 0.75 = ³⁄₄
Example 2: Convert 0.125 to a fraction
0.125 has 3 decimal places → multiply by 1000
0.125 = ¹²⁵⁄₁₀₀₀
Simplify: divide numerator and denominator by 125
Answer: 0.125 = ¹⁄₈
Example 3: Convert 0.6 to a fraction
0.6 has 1 decimal place → multiply by 10
0.6 = ⁶⁄₁₀
Simplify: divide numerator and denominator by 2
Answer: 0.6 = ³⁄₅
NB: When converting decimals with two decimal places (like 0.75), the denominator will be 100. For decimals with three decimal places (like 0.125), the denominator will be 1000.
Converting Fractions to Percentages
Percentage means "out of 100". The symbol % represents "per cent" (per hundred). To convert a fraction to a percentage, multiply the fraction by 100.
Example 1: Convert ³⁄₄ to a percentage
³⁄₄ = ³⁄₄ × 100%
= (3 × 100) ÷ 4 = 300 ÷ 4 = 75%
Answer: ³⁄₄ = 75%
Example 2: Convert ²⁄₅ to a percentage
²⁄₅ = ²⁄₅ × 100%
= (2 × 100) ÷ 5 = 200 ÷ 5 = 40%
Answer: ²⁄₅ = 40%
Example 3: Convert ⁷⁄₁₀ to a percentage
⁷⁄₁₀ = ⁷⁄₁₀ × 100%
= (7 × 100) ÷ 10 = 700 ÷ 10 = 70%
Answer: ⁷⁄₁₀ = 70%
Key Rule: Fraction to Percentage → Multiply by 100 and add the % symbol.
Converting Fractions to Decimals
To convert a fraction to a decimal, divide the numerator by the denominator.
Example 1: Convert ³⁄₄ to a decimal
Divide numerator by denominator: 3 ÷ 4
4 goes into 3 zero times → 3.00 ÷ 4 = 0.75
Answer: ³⁄₄ = 0.75
Example 2: Convert ⅕ to a decimal
Divide numerator by denominator: 1 ÷ 5
5 goes into 1 zero times → 1.0 ÷ 5 = 0.2
Answer: ⅕ = 0.2
Example 3: Convert ⅛ to a decimal
Divide numerator by denominator: 1 ÷ 8
8 goes into 1 zero times → 1.000 ÷ 8 = 0.125
Answer: ⅛ = 0.125
Converting Percentages to Decimals
To convert a percentage to a decimal, divide by 100 (move the decimal point two places to the left).
Example 1: Convert 75% to a decimal
75% = 75 ÷ 100
Move decimal point two places left: 75. → 0.75
Answer: 75% = 0.75
Example 2: Convert 40% to a decimal
40% = 40 ÷ 100
Move decimal point two places left: 40. → 0.40
Answer: 40% = 0.4
Example 3: Convert 8% to a decimal
8% = 8 ÷ 100
Move decimal point two places left: 8. → 0.08
Answer: 8% = 0.08
Converting Percentages to Fractions
To convert a percentage to a fraction, write the percentage as a fraction with denominator 100, then simplify.
Example 1: Convert 75% to a fraction
75% = ⁷⁵⁄₁₀₀
Simplify: divide numerator and denominator by 25
Answer: 75% = ³⁄₄
Example 2: Convert 40% to a fraction
40% = ⁴⁰⁄₁₀₀
Simplify: divide numerator and denominator by 20
Answer: 40% = ⅖
Example 3: Convert 12.5% to a fraction
12.5% = ¹²·⁵⁄₁₀₀
Multiply numerator and denominator by 2 to remove the decimal: ²⁵⁄₂₀₀
Simplify: divide numerator and denominator by 25
Answer: 12.5% = ⅛
Summary Table: Conversions
| Convert From | To | Operation | Example |
|---|---|---|---|
| Fraction | Decimal | Divide numerator by denominator | ¾ = 0.75 |
| Fraction | Percentage | Multiply by 100 | ¾ = 75% |
| Decimal | Fraction | Write over 10, 100, 1000, etc. depending on the number of decimal places. Then Simplify. |
0.75 = ¾ |
| Percentage | Decimal | Divide over 100 | 75% = 0.75 |
| Percentage | Fraction | Write over 100, then simplify | 75% = ¾ |
NB: Understanding conversions between fractions, decimals, and percentages is fundamental for measurement, estimation, comparison, and logical thinking. Always simplify fractions to their lowest terms, and remember that percentage means per hundred.