Lesson 2: Converting Between Percentage, Fraction & Decimal

§Text Passage

1Summary 重點摘要

Percentage, fraction and decimal are just different ways of writing the same thing. Percentage to decimal: divide by 100. Decimal to percentage: multiply by 100.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Percentage to DecimalTo change a percentage into a decimal, divide the number before the % sign by 100, which is the same as moving the decimal point two places left. Example: 60% = 60 ÷ 100 = 0.6. You can picture 60. moving to 6.0 and then 0.6; after two moves, drop the % sign and the decimal has the same value. Another example: 8% = 8 ÷ 100 = 0.08 — pad a zero on the left when the digits fall short of two places; 140% = 1.4, the whole part kept as it is, and percentages above 100% become decimals greater than 1.
2. Part 2: Decimal to PercentageTo change a decimal into a percentage, multiply the decimal by 100 and add the % sign, which moves the decimal point two places right. Example: 0.45 × 100 = 45, so with the sign it becomes 45%. Watch the places as you move: 0.45 becomes 4.5, then 45, and no extra zero is needed. Another example: 0.07 × 100 = 7, written 7%; 1.2 × 100 = 120, written 120%; decimals above 1 turn into percentages above 100%, keeping the direction consistent.
3. Part 3: Fraction to PercentageTo change a fraction into a percentage, work in two steps: first divide the numerator by the denominator to get a decimal, then multiply the decimal by 100 and add the % sign. Example: for 35, first 3 ÷ 5 = 0.6, then 0.6 × 100 = 60%, so 35 = 60%. Another example: for 720, first 7 ÷ 20 = 0.35, hence 35%; or scale the denominator to 100: 20 × 5 = 100 and the numerator 7 × 5 = 35, giving 35% as well.
4. Part 4: Percentage to FractionTo change a percentage into a fraction, first write it over 100, then simplify to lowest terms. Example: 20% = 20100; the greatest common factor of 20 and 100 is 20, and dividing both by 20 gives 15, so 20% = 15. Finding the greatest common factor is the fastest way, and the answer must be fully simplified. Another example: 45% = 45100, and dividing top and bottom by 5 gives 920; for a decimal percentage such as 12.5%, write 1251000 first, then simplify to 18.
5. Part 5: Common ConversionsSome conversions are used so often that they are worth memorising. Example: 12 = 50% = 0.5; 14 = 25% = 0.25; 34 = 75% = 0.75; 110 = 10% = 0.1; 15 = 20% = 0.2. Knowing these by heart lets you write the answer directly in a test, saving time and avoiding mistakes. Applying these common values directly in a test saves time for the other questions — the best use of your minutes.
6. Part 6: Special CasesSome fractions do not divide exactly. Example: for 13, 1 ÷ 3 = 0.333..., a recurring decimal, so the percentage is 33.33...%. Usually you round to one decimal place as the question asks, writing 33.3%, or use the fraction form 33⅓%. Always read how accurate the answer should be. Another example: 23 = 0.666..., about 66.7% as a percentage; since 66.7% does not turn back into a tidy fraction, non-terminating cases are usually answered in percentage or decimal form.
7. Part 7: CheckingGet into the habit of checking after converting. Example: if you wrote 0.25 = 25%, work backwards: 25 ÷ 100 = 0.25, which matches the original number, so the conversion is correct. If the check does not match, one step went wrong and you should work through it again. Another example: 38 = 3 ÷ 8 = 0.375, that is 37.5%; working back, 37.5 ÷ 100 = 0.375, the same as the original, so the conversion is sound.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Percentage to decimal: divide by 100
• Decimal to percentage: multiply by 100, add %
• Fraction to percentage: divide to decimal, then multiply by 100
• Percentage to fraction: write over 100, then simplify
• All three are the same value in different forms