Percentages, Fractions & Decimals Conversion

P2Percentages, Fractions and Decimals

Three ways to write the same amount.

Percentages, fractions and decimals are interchangeable — learn to switch between them.

Same value, three costumes.

50%
12
0.5

25%
14
0.25

75%
34
0.75

10%
110
0.1

% → decimal: divide by 100 · decimal → %: multiply by 100 · % → fraction: put it over 100.

Learn the Conversions

1Percentage → fraction.

Put the number over 100, then simplify.

40% = 40100 = 25

2Percentage → decimal.

Divide by 100 — digits slide two places right.

40% → 0.4

3Decimal → percentage.

Multiply by 100 — digits slide two places left.

0.7 → 70%

💡 Key IdeaAll three are the same number in different clothes. Pick whichever makes the calculation easiest.

Worked Example

Complete the family: write 60% as a fraction and a decimal.

As a fraction

60% = 60100 = 35

divide top and bottom by 20

As a decimal

60 ÷ 100 = 0.6

0.6

✓ The family

60% = 3/5 = 0.6

Watch Out! Common Mistakes

Dropping a place value.

5% = 0.5 ✕

Wrong! 5 ÷ 100 = 0.05. (0.5 is 50%.) Slide two places, not one.

Copying digits into the fraction.

40% = 140 ✕

Wrong! The percentage goes on top, over 100: 40% = 40/100 = 2/5.

Muddling 0.7 and 7%.

0.7 = 7% ✕

Wrong! 0.7 × 100 = 70%. (7% would be 0.07.)

⬇ Cheat Sheet

PERCENTAGES, FRACTIONS AND DECIMALS

% → fraction: put over 100, simplify.
% → decimal: ÷ 100 (two places right).
Decimal → %: × 100 (two places left).
Learn: 50%=1/2=0.5 · 25%=1/4=0.25 · 75%=3/4=0.75 · 10%=1/10=0.1 · 20%=1/5=0.2

Example: 60% = 60/100 = 3/5 = 0.6

📖 Continue Your Journey

✓ P1 What Are Percentages?P2 Percentages, Fractions and Decimals P3 Finding 50%, 25% and 10%P4 Percentage of an Amount P5 Percentage Increase P6 Percentage Decrease P7 Percentages and Money P8 One Number as a Percentage of Another P9 Comparing with Percentages P10 Percentage Change P11 Reverse Percentages P12 Percentage Problem Solving

→

Next Lesson: P3 Finding 50%, 25% and 10%The three percentages you can always find in your head.

📄 Free printable: Download the Percentages, Fractions and Decimals cheat sheet (PDF) — keep it by your child's desk.

Quick summary

A percentage is a fraction over 100: 40% = 40/100 = 2/5.
Percentage to decimal: divide by 100 (5% = 0.05, not 0.5).
Decimal to percentage: multiply by 100 (0.7 = 70%).
Memorise the family: 50%=1/2=0.5, 25%=1/4=0.25, 75%=3/4=0.75, 10%=1/10=0.1, 20%=1/5=0.2.

Frequently asked questions

How do you convert a percentage to a decimal?

Divide by 100 — the digits slide two places right. 40% = 0.4 and 5% = 0.05.

How do you convert a percentage to a fraction?

Write it over 100 and simplify: 60% = 60/100 = 3/5.

Which percentage facts should children memorise?

The core family: 50% = 1/2 = 0.5, 25% = 1/4 = 0.25, 75% = 3/4 = 0.75, 10% = 1/10 = 0.1 and 20% = 1/5 = 0.2. Most mental percentage work builds from these.

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P3 Finding 50%, 25% and 10%