Converting Fractions, Decimals & Percentages

Revise Converting Fractions, Decimals & Percentages for International Mathematics 0607 (O Level) — revision notes and instant AI marking.

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Summary — What This Chapter Covers

Converting percentage → decimal (÷100) and decimal → percentage (×100)
Converting a decimal → fraction using place value (tenths, hundredths, thousandths...)
Converting a percentage → fraction by writing it over 100
Converting a fraction → decimal using known facts, powers of 10, or short division
Converting a fraction → percentage (fraction → decimal → ×100)
Understanding recurring decimals and writing them with dot notation
Turning a recurring decimal into a fraction using the algebra "x = ..." method
Ordering a mix of fractions, decimals, and percentages from smallest to largest
Using inequality symbols (<, >, ≤, ≥, =, ≠) to compare values

1. The Basic FDP Conversions

Percentage ⇄ Decimal

Think of "per cent" literally — it means "per hundred". So a percentage is already a fraction out of 100 in disguise. That's why moving between percentage and decimal is just about shifting the decimal point two places.

Percentage → Decimal Divide by 100 (move digits two places right)

Worked Examples

6% ÷ 100 = 0.06

40% ÷ 100 = 0.4

350% ÷ 100 = 3.5 (percentages over 100% just mean "more than one whole")

0.2% ÷ 100 = 0.002

Decimal → Percentage Multiply by 100 (move digits two places left, add a % sign)

Worked Examples

0.35 × 100 = 35%

1.32 × 100 = 132%

0.004 × 100 = 0.4%

Why this works

Multiplying or dividing by 100 shifts every digit two "columns" — because 100 has two zeros. It's exactly the same skill as ×10 shifting one column, just doubled up.

Practice Question 1

Convert 0.045 to a percentage, and convert 215% to a decimal.

Decimal → Fraction

Every decimal is secretly a fraction with a denominator that's a power of 10 (10, 100, 1000, ...). The trick is just figuring out which power of 10 to use — and that depends on how many digits come after the decimal point.

Rule If a decimal has n digits after the decimal point, write those digits (as a whole number) over 10ⁿ. Then simplify if possible.

Decimal	Digits after point	Write over	Fraction
0.3	1	10	3/10
1.1	1	10	11/10
0.07	2	100	7/100
30.01	2	100	3001/100
0.513	3	1000	513/1000
0.0007	4	10 000	7/10 000

Watch out

Count digits after the decimal point only — not the whole number. 30.01 has two digits after the point (0 and 1), so it goes over 100, giving 3001/100 (the whole "3001" is the numerator, including the 30 whole part combined with 01).

Two special recurring decimals are worth memorising outright rather than working out each time:

0.333... (0.3 recurring) = 1/3 | 0.666... (0.6 recurring) = 2/3

And remember — any whole number can be written as a fraction just by putting it over 1. For example, 5 = 5/1.

Practice Question 2

Write 0.048 as a fraction in its simplest form.

Percentage → Fraction

Rule

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Also in the full note

2. Recurring Decimals
3. Ordering Fractions, Decimals & Percentages
What to Memorise
Concepts Checklist
Exam Tips & Common Mistakes
Fraction → Decimal
Fraction → Percentage
What Are They?

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