📚 Mastering Fractions, Decimals and Percentages for Cambridge KS3 | 剑桥KS3数学：掌握分数、小数与百分数
Fractions, decimals and percentages are three connected ways of describing a part of a whole. In the Cambridge KS3 mathematics curriculum, you are expected to convert between these forms, compare them confidently and use them in realistic problems such as discounts, data and measurement.
分数、小数和百分数是描述整体一部分的三种相互关联的方式。在剑桥 KS3 数学课程中，你需要能够在这三种形式之间进行转换、自信地比较它们，并在折扣、数据和测量等实际问题中加以运用。
1. Understanding Equivalent Forms | 理解等值形式
A fraction, a decimal and a percentage can all represent exactly the same value. For example, one half can be written as 1/2, 0.5 or 50%. These are called equivalent forms because they describe the same part of a whole.
分数、小数和百分数可以表示完全相同的值。例如，一半可以写成 1/2、0.5 或 50%。这些被称为等值形式，因为它们描述的是同一个整体部分。
1/2 = 0.5 = 50%
A fraction has a numerator above a denominator, such as 3/4. A decimal uses place value columns after the point, including tenths, hundredths and thousandths. A percentage is simply a number of parts out of 100.
分数在分母上方有分子，例如 3/4。小数使用小数点后的位值列，包括十分位、百分位和千分位。百分数只是每一百份中的份数。
Understanding this equivalence helps you choose the most useful form for a problem. For example, multiplying by a decimal is often easier than multiplying by a fraction, while a percentage is easier to interpret in a sales sign.
理解这种等值关系可以帮助你为问题选择最合适的形式。例如，用小数相乘通常比用分数相乘更容易，而百分数在销售标牌上更容易理解。
2. Converting Fractions to Decimals | 分数转小数
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/8 means 3 ÷ 8, which gives 0.375. This method works for any fraction.
要将分数转换为小数，用分子除以分母。例如，3/8 表示 3 ÷ 8，得到 0.375。这个方法适用于任何分数。
3/8 = 3 ÷ 8 = 0.375
ator directly in the correct decimal place. For example, 7/100 = 0.07 and 23/1000 = 0.023.
当分母是 10、100 或 1000 时，你可以将分子直接写在正确的小数位上。例如，7/100 = 0.07，23/1000 = 0.023。
estions, a recurring decimal is often shown with a dot above the repeating digit or with three dots after the number.
一些分数会产生循环小数。例如，1/3 = 0.333...，2/9 = 0.222...。在剑桥 KS3 题目中，循环小数通常用重复数字上方的点或用数字后的三个点表示。
mber to an improper fraction first if you need to divide. For example, 1 3/4 = 7/4 = 1.75.
如果需要相除，先把带分数转换为假分数也很有帮助。例如，1 3/4 = 7/4 = 1.75。
3. Converting Decimals to Percentages | 小数转百分数
the decimal by 100 and write the percent sign. For example, 0.45 × 100 = 45, so 0.45 = 45%.
要将小数转换为百分数，将小数乘以 100 并写上百分号。例如，0.45 × 100 = 45，所以 0.45 = 45%。
0.45 × 100 = 45%
This works because hundredths in a decimal already mean parts per hundred. A decimal such as 0.07 is exactly 7 hundredths, so it equals 7%.
这是因为小数中的百分位已经表示每一百份中的份数。像 0.07 这样的小数正好是 7 个百分之一，所以它等于 7%。
For decimals greater than 1, the percentage is greater than 100. For example, 1.25 = 125% and 2.8 = 280%. This often appears in percentage increase questions.
对于大于 1 的小数，百分数大于 100。例如，1.25 = 125%，2.8 = 280%。这通常出现在百分数增加的题目中。
When converting a decimal such as 0.6 to a percentage, you can think of it as
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