📚 KS3 Cambridge Mathematics: Fractions, Decimals and Percentages | KS3 剑桥数学：分数、小数和百分数
Working confidently with fractions, decimals and percentages is one of the most important skills in the Cambridge KS3 mathematics curriculum. These three forms describe the same proportional idea, but many mixed exercises, including page 198 question 2, test your ability to convert, compare and apply them in real situations. In this article, you will review the key methods, see worked examples and practise common exam-style problems.
在剑桥 KS3 数学课程中，熟练处理分数、小数和百分数是最重要的技能之一。这三种形式描述的是同一个比例概念，但许多综合练习，包括第198页第2题，会考查你的换算、比较和实际应用能力。本文将复习核心方法，给出典型例题，并练习常见考试题型。
1. Understanding the Core Equivalences | 理解核心等值关系
A fraction, a decimal and a percentage can all represent the same part of a whole. For example, one half can be written as 1/2, 0.5 or 50%. You should memorise common equivalences because they speed up mental calculation and help you check written work.
分数、小数和百分数都可以表示同一个整体的一部分。例如，二分之一可以写成 1/2、0.5 或 50%。你应当熟记常见等值关系，因为它们能加快心算速度，也有助于检查笔算结果。
| Fraction | Decimal | Percentage |
|---|---|---|
| 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% |
When you see a mixed list of fractions, decimals and percentages, the safest first step is to convert every value to the same form. This removes the risk of comparing unlike forms and makes ordering much easier.
当你看到分数、小数和百分数混合的一组数时，最稳妥的第一步是把每个值都转换成同一种形式。这可以避免比较不同形式带来的错误，并使排序更加容易。
2. Converting Fractions to Decimals | 分数化小数
75. If the denominator does not divide neatly into a power of ten, long division gives the exact or recurring decimal.
将分数化为小数，只需用分子除以分母。对于 3/8 这样的简单分数，计算 3 ÷ 8 = 0.375。如果分母不能整除 10 的幂，则用长除法得到精确小数或循环小数。
decimal places matches the number of zeros. For example, 47/100 = 0.47 and 9/1000 = 0.009.
对于分母已经是 10、100 或 1000 的分数，只需把分子放在小数点后面，并使小数位数与零的个数一致。例如 47/100 = 0.47，9/1000 = 0.009。
fraction → decimal: numerator ÷ denominator
中文：分数化小数：分子除以分母。
3. Converting Decimals to Percentages | 小数化百分数
Percent means 'out of 100' Move the decimal point two places to the right. For instance, 0.85 becomes 0.85 × 100 = 85%, while 0.035 becomes 3.5%.
百分数表示“每一百份中的多少”，因此小数化为百分数只需乘以 100，也就是把小数点向右移动两位。例如，0.85 乘以 100 得 85%，而 0.035 得 3.5%。
Remember that numbers larger than 1 give percentages greater than 100%. For example, 1.2 = 120% ssume that percentages must be less than 100; mixed numbers often produce values above 100%.
请记住，大于 1 的数对应的百分数会超过 100%。例如 1.2 = 120%，因为 1.2 × 100 = 120。不要认为百分数一定小于 100；带分数常常会产生超过 100% 的值。
4. Converting Percentages to Fractions | 百分数化分数
rite a percentage as a fraction, put the percentage over 100 and simplify. For example, 45% erator and denominator by 5. If the percentage contains a decimal, multiply the numerator and denominator by 10 or 100 first.
将百分数写成分数时，先把百分数写在 100 的上方，然后约分。例如 45% = 45/100，分子分母同除以 5 后得到 9/20。如果百分数含有小数，应先给分子分母同乘 10 或 100。
For 12.5%, write 12.5/100 and multiply top and bottom by 10 to obtain 125/1000, which simplifies to 1/8. This trick removes the decimal from the numerator and makes simplification straightforward.
对于 12.5%，可写成 12.5/100，再将分子分母同乘以 10 得到 125/1000，最后约分成 1/8。这个方法可以消去分子中的小数点，使约分更直接。
5. Ordering Mixed Numbers | 混合数排序
first. Decimals are easy to compare place by place. For example, to order 3/5, 0.58 and 62%, convert: 3/5 = 0.6, 0.58 = 0.58, 62% = 0.62. Then ascending order is 0.58, 0.6, 0.62, so 0.58, 3/5, 62%.
当题目要求把一组分数、小数和百分数按顺序排列时，先把它们都化成小数。小数按数位逐位比较非常方便。例如，要排序 3/5、0.58 和 62%，先转换：3/5 = 0.6，0.58 = 0.58，62% = 0.62。因此从小到大依次为 0.58、0.6、0.62，即 0.58、3/5、62%。
Use zero placeholders to avoid mistakes when comparing decimals. For example, write 0.6 as 0.60 so you can see that 0.58 is smaller than
Published by TutorHao | KS3 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