📚 IGCSE Maths: Number – Fractions, Decimals and Percentages | IGCSE 数学：数与分数、小数和百分比
Fractions, decimals and percentages are three connected ways of describing parts of a whole. In IGCSE Mathematics, this topic appears across the Core and Extended papers, from straightforward conversions to reverse percentage and repeated change problems.
分数、小数和百分比是描述整体中部分数量的三种相互关联的方式。在 IGCSE 数学中，这一主题贯穿核心卷和扩展卷，从直接换算到逆向百分比与重复变化问题都会涉及。
1. Core Concepts | 核心概念
A fraction is written as a/b, where a is the numerator and b is the denominator. A decimal uses the base-ten place value system, while a percentage is a ratio compared with 100. Being able to switch between these forms quickly is an essential skill.
分数写作 a/b，其中 a 是分子，b 是分母。小数使用以十为基数的位值系统，百分比则是与 100 比较的比例。能够在这三种形式之间快速转换是一项核心技能。
The following equivalence facts are expected knowledge at IGCSE level and should be memorised.
以下等价关系是 IGCSE 阶段要求掌握的知识，应当熟记。
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
2. Converting Fractions to Decimals | 分数转小数
oduce terminating decimals, while others produce recurring decimals such as 1/3 = 0.333...
用分子除以分母即可将分数转换为小数。例如，3/8 等于 3 ÷ 8，结果为 0.375。有些分数会得到有限小数，有些则会产生循环小数，例如 1/3 = 0.333...
3/8 = 3 ÷ 8 = 0.375
Use a calculator for difficult divisions, but always check whether the question requires an exact answer or a rounded value. If rounding is needed, state the degree of accuracy clearly, such as 0.33 to 2 decimal places.
遇到较难的除法时可以使用计算器，但一定要检查题目要求的是精确值还是近似值。如果需要四舍五入，请清楚说明精度，例如精确到两位小数为 0.33。
3. Converting Decimals to Percentages | 小数转百分比
uivalent to moving the decimal point two places to the right. For example, 0.47 × 100 = 47%.
将小数乘以 100 并加上百分号。这相当于把小数点向右移动两位。例如，0.47 × 100 = 47%。
0.47 = 0.47 × 100% = 47%
ercentage back to a decimal, divide by 100 and remove the percentage sign. Remember that 8% = 0.08, 2.5% = 0.025 and 0.3% = 0.003.
将百分比转换回小数时，除以 100 并去掉百分号。请记住 8% = 0.08，2.5% = 0.025，0.3% = 0.003。
2.5% = 2.5 ÷ 100 = 0.025
4. Converting Percentages to Fractions | 百分比转分数
n simplify by dividing the numerator and denominator by any common factor. For example, 45% = 45/100 = 9/20.
把百分比写成分母为 100 的分数，然后通过同除公因数进行约分。例如，45% = 45/100 = 9/20。
45% = 45/100 = 9/20
imal, multiply both numerator and denominator by 10, 100 or 1000 first. For instance, 12.5% = 12.5/100 = 125/1000 = 1/8.
如果百分比含有小数，应先将分子和分母同乘以 10、100 或 1000。例如，12.5% = 12.5/100 = 125/1000 = 1/8。
12.5% = 125/1000 = 1/8
5. Ordering Mixed Forms | 混合形式的排序
When comparing fractions, decimals and percentages, convert every value into the same form. Decimals are often the fastest choice. For example, compare 2/5, 0.39 and 41%.
比较分数、小数和百分比时，应把所有数值转换为同一种形式。通常转换为小数最快。例如，比较 2/5、0.39 和 41%。
2/5 = 0.400, 41% = 0.410 → 0.39 < 2/5 < 41%
and 5/11, calculate 3 × 11 = 33 and 5 × 7 = 35. Since 33 < 35, it follows that 3/7 < 5/11.
比较不同分母的分数时，可以使用交叉相乘。比较 3/7 和 5/11，计算 3 × 11 = 33，5 × 7 = 35。因为 33 < 35，所以 3/7 < 5/11。
6. Adding and Subtracting Fractions | 分数加减法
1/4, the lowest common denominator is 12, so 2/3 = 8/12 and 1/4 = 3/12. The sum is 11/12.
进行加减运算前，先将各分数化为
Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图