📚 Fractions, Decimals and Percentages (T-1-1020) | IGCSE 数学：分数、小数与百分数（T-1-1020）
In IGCSE Mathematics, you must move confidently between fractions, decimals and percentages. Many exam questions mix all three forms, so quick and accurate conversion is essential for number, proportion and data handling topics. This revision guide covers the core methods, common pitfalls and exam techniques you need to master this part of the syllabus.
在 IGCSE 数学中，你必须能在分数、小数和百分数之间熟练转换。很多考题会混合这三种形式，因此快速准确的转换对于数、比例和数据处理主题至关重要。本复习指南涵盖你需要掌握的核心方法、常见错误和考试技巧。
1. The Big Picture: How Fractions, Decimals and Percentages Connect | 整体框架：分数、小数和百分数如何联系
All three forms represent the same idea: a part of a whole. A fraction compares a part to a whole using a numerator and denominator, a decimal uses base-ten place value, and a percentage is simply a fraction with denominator 100. Understanding this link makes conversion logical rather than a set of separate rules.
三种形式都表示同一个概念：整体的一部分。分数用分子和分母表示部分与整体的比较，小数使用十进制的位值，而百分数就是分母为 100 的分数。理解这种联系会使转换更有逻辑，而不是彼此孤立的规则。
2. Fraction to Decimal: Divide the Numerator by the Denominator | 分数转小数：分子除以分母
xed numbers, keep the whole number part and convert the proper fraction, so 2 3/8 = 2.375.
分数线就是除号。将 3/8 转换为小数，计算 3 ÷ 8 = 0.375。对于带分数，保留整数部分，只转换真分数部分，因此 2 3/8 = 2.375。
3. Decimal to Fraction: Use Place Value | 小数转分数：使用位值
Write the decimal as a fraction over 10, 100, 1000 and so on, according to the last digit' xample, 0.65 = 65/100 = 13/20. Always simplify fully unless the question states otherwise.
根据最后一位数字的位值，将小数写成分母为 10、100、1000 等的分数。例如 0.65 = 65/100 = 13/20。除非题目另有说明，否则一定要化简到最简。
4. Recurring Decimals to Fractions | 循环小数转分数
23..., so 99x = 23 and x = 23/99. Use powers of ten that match the repeating block length.
对于循环小数如 0.232323...，设 x = 0.2323...。乘以 100 得 100x = 23.2323...。然后相减：100x - x = 23.2323... - 0.2323...，因此 99x = 23，x = 23/99。使用与循环节长度匹配的 10 的幂。
5. Decimal to Percentage and Percentage to Decimal | 小数与百分数互转
Multiply by 100 to change a decimal to a percentage: 0.47 × 100 = 47%. Divide by 100 to change a percentage to a decimal: 85% = 85 ÷ 100 = 0.85. Moving the decimal point two places is a fast shortcut.
小数转百分数乘以 100：0.47 × 100 = 47%。百分数转小数除以 100：85% = 85 ÷ 100 = 0.85。将小数点移动两位是快速技巧。
6. Fraction to Percentage: Use a Denominator of 100 or Convert via Decimal | 分数转百分数：用分母 100 或先转小数
You can create an equivalent fraction with denominator 100, such as 3/25 = 12/100 = 12% rst divide to get a decimal then multiply by 100. For 2/7, 2 ÷ 7 ≈ 0.285714, so 2/7 ≈ 28.6% to one decimal place.
你可以先构造分母为 100 的等值分数，例如 3/25 = 12/100 = 12%。如果不容易，先除法得到小数再乘以 100。对于 2/7，2 ÷ 7 ≈ 0.285714，所以 2/7 ≈ 28.6%（保留一位小数）。
7. Ordering Fractions, Decimals and Percentages | 比较分数、小数和百分数的大小
usually decimals or percentages. Compare values place by place. For example, 3/5 = 0.6, 55% = 0.55, and 0.7 = 0.7, so the ascending order is 55%, 3/5, 0.7.
要比较混合形式，先将所有数值转换为同一种形式，通常是小数或百分数。按位值逐一比较。例如 3/5 = 0.6，55% = 0.55，0.7 = 0.7，所以从小到大为 55%、3/5、0.7。
8. Common Conversions You Must Know | 必须熟记的常见转换
Memorising these common conversions speeds up calculation and checking. Use them to estimate answers and spot mistakes in both non-calculator and calculator papers.
熟记这些常见转换能加快计算和检查。用它们来估算答案，并在非计算器和计算器试卷中发现问题。
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/3 | 0.333... | 33.3% |
| 2/3 | 0.666... | 66.7% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
9. Worked Exam-Style Example | 考试题型示例
Question: Express 0.375 as a fraction in its lowest terms, then find 0.375 + 45% as a decimal. Solution: 0.375 = 375/1000 = 3/8. 45% = 0.45. Sum = 0.375 + 0.45 = 0.825.
问题：将 0.375 表示为最简分数，再求 0.375 + 45% 的小数结果。解：0.375 = 375/1000 = 3/8。45% = 0.45。和 = 0.375 + 0.45 = 0.825。
10. Common Mistakes and Exam Tips | 常见错误与考试技巧
Do not add denominators when adding fractions; convert to a common denominator first. Do not confuse 0.5% with 0.5. Always check recurring decimal notation and simplify fractions fully. Show method for recurring decimal questions because the proof uses subtraction.
分数相加时不要直接加分母；先转换成同分母。不要混淆 0.5% 与 0.5。始终检查循环小数的记法，并将分数完全化简。循环小数题要写出过程，因为证明用到相减。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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