📚 Mastering Percentages, Percentage Change and Compound Interest for IGCSE Mathematics | IGCSE 数学：百分数、百分比变化与复利
Percentages appear throughout IGCSE Mathematics, from basic conversions to multi-step reverse percentage problems and compound interest models. This article builds the skills step by step, including common pitfalls and exam-style strategies.
百分数贯穿 IGCSE 数学始终，从基本换算到多步骤反向百分数问题和复利模型。本文逐步构建技能，包括常见误区和考试策略。
1. The Meaning of Percent and Key Conversions | 百分数的含义与关键换算
A percentage is a ratio expressed as a fraction of 100. The symbol % means 'per cent', or 'out of 100'. In IGCSE problems, you must be able to move quickly between percentages, decimals and fractions.
百分数是以 100 为分母的比率。符号 % 表示 '每一百'。在 IGCSE 题目中，你必须能在百分数、小数和分数之间快速转换。
| Form | Rule | Example |
|---|---|---|
| Percent → decimal | divide by 100 | 7% = 0.07 |
| Decimal → percent | multiply by 100 | 0.35 = 35% |
| Percent → fraction | write over 100 and simplify | 25% = 25/100 = 1/4 |
| Fraction → percent | multiply by 100 | 3/5 × 100% = 60% |
To convert a fraction such as 3/5 into a percentage, multiply by 100:
要将 3/5 这样的分数转换为百分数，乘以 100：
3/5 × 100% = 60%
2. Finding a Percentage of a Quantity | 求一个量的百分数
To find a% of a quantity, change a% decimal by dividing by 100, then multiply. For mental arithmetic, learn key benchmarks: 50% = 1/2, 25% = 1/4, 10% = 1/10, 1% = 1/100.
要求一个量的 a%，先把 a% 改成小数（除以 100）再相乘。心算时记住关键基准：50% = 1/2，25% = 1/4，10% = 1/10，1% = 1/100。
Example: Find 15% of 240 kg. Since 15% = 0.15, calculate 0.15 × 240 = 36 kg.
例题：求 240 kg 的 15%。因为 15% = 0.15，计算 0.15 × 240 = 36 kg。
Using benchmarks can be quicker: 10% of 240 is 24, 5% is 12, so 15% = 24 + 12 = 36.
使用基准值可以更快：240 的 10% 是 24，5% 是 12，所以 15% = 24 + 12 = 36。
