📚 Percentages, Reverse Percentages and Compound Interest | 百分比、逆运算与复利
Percentages are one of the most practical tools in IGCSE Mathematics. They appear in financial contexts such as discounts, tax, interest, depreciation, and in data comparisons. This revision guide explains how to convert between fractions, decimals and percentages, calculate percentage change, work backwards with reverse percentages, and apply repeated percentage change including compound interest and depreciation.
百分比是 IGCSE 数学中最实用的工具之一，常出现在折扣、税收、利息、折旧等金融情境以及数据比较中。本复习指南将讲解如何在不同形式间转换，计算百分比变化，使用逆运算求原值，并应用重复百分比变化，包括复利和折旧。
1. Fractions, Decimals and Percentages | 分数、小数与百分比
A percentage means 'out of 100', so 35% means 35/100 or 0.35. To convert a decimal to a percentage, multiply by 100, moving the decimal point two places to the right. To convert a percentage to a decimal, divide by 100. To convert a fraction to a percentage, divide the numerator by the denominator and then multiply by 100.
百分比表示“每一百份中的多少”，因此 35% 表示 35/100 或 0.35。将小数转换为百分比时乘以 100，也就是把小数点向右移动两位；将百分比转换为小数时除以 100。将分数转换为百分比时，先计算分子除以分母，再乘以 100。
For example, 7/20 = 7 ÷ 20 = 0.35, and 0.35 × 100 = 35%. Memorise common equivalents such as 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, and 1/10 = 0.1 = 10%.
例如，7/20 = 7 ÷ 20 = 0.35，再乘以 100 得到 35%。应熟记常见等价关系：1/2 = 0.5 = 50%，1/4 = 0.25 = 25%，3/4 = 0.75 = 75%，1/5 = 0.2 = 20%，1/10 = 0.1 = 10%。
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