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 decimal to a percentage by multiplying by 100
Convert decimals greater than 1 to percentages greater than 100%
Use decimal-to-percentage conversion in context (e.g. test results)
Understand the relationship between the ×100 and ÷100 conversions
Real-World Applications
Science: An experiment gives a result of 0.82. Expressing this as 82% makes it meaningful in a report.
Statistics: A probability of 0.35 is better communicated to the public as 35%.
Finance: A stock price multiplier of 1.06 means a 6% increase.
The Core Rule: Multiply by 100
Converting a decimal to a percentage is the reverse of converting a percentage to a decimal. Instead of dividing by 100, you multiply by 100. Multiplying by 100 moves the decimal point 2 places to the right.
Common mistake: Moving the decimal point the wrong way. To convert decimal → percentage, move RIGHT 2 places (multiply). To convert percentage → decimal, move LEFT 2 places (divide).
Example 3b — The round trip: convert 0.35 to a percentage, then back to a decimal
You land back on the number you started with — ×100 and ÷100 are inverse operations, so they always undo each other exactly.
✓ Quick Check 1 — Simple decimals to percentages
Question 1 of 10
Decimals Greater Than 1 → Percentages Greater Than 100%
If a decimal is greater than 1, the percentage will be greater than 100%. This is common in growth, profit, and ratio contexts.
Example 4 — Convert 1.4 to a percentage
1
\(1.4 \times 100\)
2
Answer: \(\mathbf{140\%}\)
Example 5 — Convert 2.05 to a percentage
1
\(2.05 \times 100 = 205\)
2
Answer: \(\mathbf{205\%}\)
Context example: A company's profit multiplier is 1.15, which means profit grew to 115% of its previous value — a 15% increase. To find the percentage increase: \(1.15 \times 100 = 115\%\), so the increase = \(115 - 100 = 15\%\).
✓ Quick Check 2 — Harder decimals and > 1
Question 1 of 10
Applying Decimal-to-Percentage in Context
A common exam application is expressing a score or proportion as a percentage.
Example 6 — A student scored 34 out of 40. Express this as a percentage.
1
Write as a fraction: \(\frac{34}{40}\)
2
Convert to decimal: \(34 \div 40 = 0.85\)
3
Convert to percentage: \(0.85 \times 100 = 85\%\)
4
Answer: \(\mathbf{85\%}\)
Example 7 — Compare 0.72 and 69% — which is larger?
1
Convert 0.72 to a percentage: \(0.72 \times 100 = 72\%\)
2
Compare: \(72\% > 69\%\)
3
Answer: \(\mathbf{0.72}\) is larger
Example 8 — Express 0.006 as a percentage
1
\(0.006 \times 100\)
2
Move decimal 2 places right: 0.006 → 0.6
3
Answer: \(\mathbf{0.6\%}\)
The FDP triangle: Fraction ↔ Decimal (divide numerator by denominator). Decimal ↔ Percentage (× 100 or ÷ 100). Fraction ↔ Percentage (× 100 or ÷ 100). All three forms express the same proportion.
✓ Quick Check 3 — Real-life and context
Question 1 of 10
Practice: Convert these decimals to percentages
Type your answer with % (e.g. 45%), then click Check.
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Question
Answer
Result
1
Convert 0.63 to a percentage
2
Convert 0.07 to a percentage
3
Convert 0.375 to a percentage
4
Convert 1.4 to a percentage
5
Convert 2.05 to a percentage
6
A student scored 34 out of 40. Express this as a percentage.
7
Convert 0.006 to a percentage
8
Convert 0.9 to a percentage
9
Convert 0.125 to a percentage
10
Convert 3.5 to a percentage
⚠ Things to Watch Out For
Forgetting to multiply by 100: Decimal to percentage always means × 100 — moving the decimal point only one place instead of two is a common slip.
Decimals over 1 give percentages over 100%: This is correct, not an error — e.g. 1.4 = 140%.
Very small decimals: 0.006 = 0.6%, not 6% — count the decimal places carefully when the value is small.
Confusing the direction: Decimal to percentage moves the point RIGHT two places. Moving it left converts the other way (percentage to decimal).
Forgetting the % symbol: The final answer must include the % sign — writing just the number is incomplete.