Fractions, decimals and percentages are three ways to write the same amount. The repair is to stop treating them as three topics and always route through one common form: hundredths.
What is the small gap usually hiding?
The student knows 3/4 is “three quarters” and knows 75% exists, but has no route between them. Each question then becomes a guess about which way to shift the decimal point.
A percentage means “out of 100”. So percentage, decimal and fraction connect like this.
| Form | Example | Reads as |
|---|---|---|
| Fraction | 3/8 | 3 divided by 8 |
| Decimal | 0.375 | 375 thousandths |
| Percentage | 37.5% | 37.5 out of 100 |
How do you convert step by step?
Start with a fraction, because the fraction is the instruction: the top number divided by the bottom number.
- Fraction to decimal: divide the numerator by the denominator.
- Decimal to percentage: multiply by 100, which moves the point two places right.
- Percentage to decimal: divide by 100, which moves the point two places left.
- Percentage to fraction: write it over 100, then simplify.
A scaffolded example
An original question: in a Form 4 class of 40, 14 students cycle to school. What percentage cycles?
The fraction is 14/40. Divide: 14 ÷ 40 = 0.35. Multiply by 100: 0.35 × 100 = 35%.
Check with a rough size. 14 is a little less than half of 40 (which is 20), so the answer should be a little below 50%. 35% fits.
What does the common mistake look like?
A student writes 14/40 = 14 × 40 ÷ 100 = 5.6%. The idea was “multiply and divide by something”, but the operations came from memory rather than meaning.
The rough-size check exposes it at once: 5.6% is far too small for nearly half a class. Meaning first, then the keystrokes.
Self-check
Write 0.06 as a percentage, and 7/20 as a decimal and a percentage.
Answer
0.06 × 100 = 6%. Note this is 6%, not 60%: the decimal 0.06 has a zero in the tenths place.
7/20: 7 ÷ 20 = 0.35, so 35%. Quick check: 7/20 is between 1/4 (25%) and 1/2 (50%), and 35% sits there.
Where does this show up in SPM?
In SPM Mathematics, it appears in discount and tax questions, in statistics and in probability answers written as percentages. In Science, it appears in percentage yield, efficiency and composition calculations.
The next step is percentage increase and decrease, which assumes today’s skill. Return to the fractions, decimals and percentages hub to see the full order, or try the prerequisite gap finder to locate other weak spots.
If the slip keeps returning, online one-to-one SPM Mathematics tuition starts with a one-hour trial class (from RM50).