Fractions, Decimals and Percentages are three ways of writing the same value. The triangle below shows how to move between them.
Learning Objectives
Convert a percentage to a decimal by dividing by 100
Use the decimal point shift method (move 2 places left)
Convert percentages greater than 100% to decimals greater than 1
Convert percentages less than 1% to small decimals
Real-World Applications
Percentage calculations: To find 35% of £240, first convert 35% to 0.35, then calculate \(0.35 \times 240\).
Interest rates: A bank offers 4.5% interest — as a multiplier this is 0.045.
Discounts: A 20% discount means multiplying the price by 0.2 to find the reduction, or by 0.8 to find the new price.
The Core Rule: Divide by 100
"Per cent" means out of 100. So to convert a percentage to a decimal, divide by 100. Dividing by 100 moves the decimal point 2 places to the left.
\[\text{Decimal} = \text{Percentage} \div 100\]
Example 1 — Convert 37% to a decimal
1
37% means 37 out of 100
2
\(37 \div 100 = 0.37\)
3
Decimal point moves 2 places left: 37. → 0.37
4
Answer: \(\mathbf{0.37}\)
Example 2 — Convert 8% to a decimal
1
\(8 \div 100\)
2
Move decimal point 2 places left: 8. → 0.08
3
Answer: \(\mathbf{0.08}\)
Common mistake: Writing 8% as 0.8 (only moving 1 place). Single-digit percentages need a leading zero: 8% = 0.08, NOT 0.8.
Example 3 — Convert 7% to a decimal
1
\(7 \div 100\)
2
Move decimal 2 places left: 7. → 0.07
3
Answer: \(\mathbf{0.07}\)
Example 4 — Convert 130% to a decimal
1
\(130 \div 100\)
2
Move decimal 2 places left: 130. → 1.30 = 1.3
3
Answer: \(\mathbf{1.3}\)
Percentage
÷ 100
Decimal
50%
50 ÷ 100
0.5
25%
25 ÷ 100
0.25
75%
75 ÷ 100
0.75
10%
10 ÷ 100
0.1
5%
5 ÷ 100
0.05
1%
1 ÷ 100
0.01
33.3%
33.3 ÷ 100
0.333...
✓ Quick Check 1 — Integer percentages to decimals
Question 1 of 10
Percentages Greater Than 100%
Percentages greater than 100% give decimals greater than 1. These arise in contexts like growth, percentage increase, or when comparing a new value to an original.
Example 5 — Convert 150% to a decimal
1
\(150 \div 100\)
2
Move decimal 2 places left: 150. → 1.50 = 1.5
3
Answer: \(\mathbf{1.5}\)
Example 6 — Convert 112.5% to a decimal
1
\(112.5 \div 100 = 1.125\)
2
Answer: \(\mathbf{1.125}\)
Application: A price increases by 12%. The multiplier for the new price is \(100\% + 12\% = 112\% = 1.12\). So new price = original × 1.12.
✓ Quick Check 2 — Decimal percentages and harder conversions
Question 1 of 10
Percentages Less Than 1%
Very small percentages (like 0.5% or 0.25%) give very small decimals. Be especially careful with the decimal point position.
Example 7 — Convert 0.5% to a decimal
1
\(0.5 \div 100\)
2
Move decimal 2 places left: 0.5 → 0.005
3
Answer: \(\mathbf{0.005}\)
Example 7b — Convert 0.25% to a decimal
1
\(0.25 \div 100\)
2
Move decimal 2 places left: 0.25 → 0.0025
3
Answer: \(\mathbf{0.0025}\) — notice this one needs two leading zeros before the first non-zero digit, since 0.25 only has 2 digits to shift past.
Example 8 — Using the decimal multiplier to calculate a percentage
Find 35% of £840.
1
Convert: 35% = 0.35
2
\(0.35 \times 840 = 294\)
3
Answer: £294
Multiplier method: Converting a percentage to a decimal is the first step in calculating any percentage of an amount. Learn to do this confidently — it appears in almost every percentage question.
✓ Quick Check 3 — Mixed and real-life
Question 1 of 10
Practice: Convert these percentages to decimals
Type your decimal answer (e.g. 0.45), then click Check.
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Question
Answer
Result
1
Convert 37% to a decimal
2
Convert 8% to a decimal
3
Convert 7% to a decimal
4
Convert 130% to a decimal
5
Convert 150% to a decimal
6
Convert 112.5% to a decimal
7
Convert 0.5% to a decimal
8
Convert 45% to a decimal
9
Convert 200% to a decimal
10
Convert 6.25% to a decimal
⚠ Things to Watch Out For
Forgetting to divide by 100: Percentage to decimal always means ÷ 100 — dividing by 10 instead is a very common slip.
Percentages over 100%: A percentage greater than 100% converts to a decimal greater than 1 (e.g. 150% = 1.5) — this is correct, not a mistake.
Small percentages need extra zeros: 0.5% = 0.005, not 0.05. Count the decimal place shift carefully for percentages under 1%.
Moving the decimal point the wrong way: Percentage to decimal moves the point LEFT two places. Moving it right converts the other way (decimal to percentage).
Dropping trailing detail: Write the full decimal, including any necessary zeros — 8% is 0.08, not 0.8.