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O Level · Mathematics 0580

Working with FDP

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Converting Fractions, Decimals & Percentages

Understanding FDP

Fractions, decimals, and percentages are three different ways to represent the same amounts. For example, ½, 0.5, and 50% all represent the same value. Being able to convert between these forms fluently is essential for IGCSE maths.

Why three forms? Different forms are useful in different contexts. Fractions are exact and good for theoretical work. Decimals are convenient for calculations. Percentages are perfect for real-world comparisons (like discounts or interest rates).

Percentage ↔ Decimal

Percentage to Decimal

Divide by 100. This moves the decimal point two places to the left.

Percentage to Decimal Percentage ÷ 100 = Decimal

Examples

6% → 6 ÷ 100 = 0.06

40% → 40 ÷ 100 = 0.4

350% → 350 ÷ 100 = 3.5

0.2% → 0.2 ÷ 100 = 0.002

Decimal to Percentage

Multiply by 100. This moves the decimal point two places to the right.

Decimal to Percentage Decimal × 100 = Percentage (with % sign)

Examples

0.35 → 0.35 × 100 = 35%

1.32 → 1.32 × 100 = 132%

0.004 → 0.004 × 100 = 0.4%

Decimal ↔ Fraction

Decimal to Fraction

Count the number of decimal places. Write the digits as the numerator and use 10^n as the denominator (where n is the number of decimal places). Simplify if needed.

Decimal to Fraction (n = number of decimal places) One decimal place: ÷ 10
Two decimal places: ÷ 100
Three decimal places: ÷ 1000
n decimal places: ÷ 10ⁿ

Examples

0.3 = 3/10

0.07 = 7/100

0.513 = 513/1000

0.0007 = 7/10,000

Fraction to Decimal

Divide the numerator by the denominator. You can either use a calculator or do short division. It's helpful to know some common fractions by heart.

Common Fractions You Must Know

1/2 = 0.5 | 1/4 = 0.25 | 3/4 = 0.75 | 1/5 = 0.2 | 2/5 = 0.4 | 3/5 = 0.6 | 4/5 = 0.8

1/3 = 0.333... | 2/3 = 0.666... | 1/10 = 0.1 | 1/8 = 0.125

Shortcut: Fractions Over Powers of 10

If the denominator is a factor of 10, 100, 1000, etc., you can convert to a power of 10 denominator, then to decimal instantly.

Examples

3/5 = 6/10 = 0.6

7/20 = 35/100 = 0.35

1/500 = 2/1000 = 0.002

Percentage ↔ Fraction

Percentage to Fraction

Write the percentage number as the numerator and 100 as the denominator. Simplify if possible.

Percentage to Fraction

Examples

37% = 37/100

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Also in the full note

Recurring Decimals
Ordering Fractions, Decimals & Percentages
Summary & Review
Concepts Checklist
What to Memorize
Exam Tips & Strategy
Simple Recurring Decimals as Fractions
What Are Recurring Decimals?

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Working with FDP

Working with FDP

Converting Fractions, Decimals & Percentages

Understanding FDP

Percentage ↔ Decimal

Percentage to Decimal

Decimal to Percentage

Decimal ↔ Fraction

Decimal to Fraction

Fraction to Decimal

Shortcut: Fractions Over Powers of 10

Percentage ↔ Fraction

Percentage to Fraction

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