Fractions, Decimals and Percentages: IGCSE Core Skills | 分数、小数和百分比：IGCSE 核心技能

📚 Fractions, Decimals and Percentages: IGCSE Core Skills | 分数、小数和百分比：IGCSE 核心技能

Fractions, decimals and percentages are three equivalent ways of expressing parts of a whole. In IGCSE Mathematics, you must be able to move fluently between them, compare values accurately, and apply percentage change in practical contexts such as discounts, interest and data interpretation.

分数、小数和百分比是表示整体部分的三种等价方式。在 IGCSE 数学中，你需要能够在它们之间熟练转换、准确比较大小，并在折扣、利息和数据分析等实际情境中应用百分比变化。

1. Understanding the Three Forms | 理解三种表示形式

A fraction uses a numerator over a denominator, such as 3/4, to show 3 parts out of 4 equal parts. A decimal uses place value and a decimal point, such as 0.75. A percentage means ‘out of 100’, so 75% means 75 out of 100 equal parts.

分数用分子除以分母表示，例如 3/4，表示 4 等份中的 3 份。小数使用位值和小数点，例如 0.75。百分比表示“每一百中的多少”，因此 75% 表示 100 等份中的 75 份。

These three forms are interchangeable. Being able to switch between them is essential for ordering values, calculating discounts, interpreting data, and solving proportion questions across the IGCSE syllabus.

这三种形式可以互相转换。能够在它们之间切换对于排序、计算折扣、解读数据以及解答 IGCSE 大纲中的比例问题都至关重要。

• A fraction is a division: 3/4 means 3 ÷ 4.
  分数是一种除法：3/4 表示 3 ÷ 4。
• A decimal uses tenths, hundredths and thousandths based on place value.
  小数根据位值使用十分位、百分位和千分位。
• A percentage is a ratio compared with 100.
  百分比是与 100 相比的比率。

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 = 3 ÷ 8 = 0.375.

要把分数转换为小数，用分子除以分母。例如，3/8 = 3 ÷ 8 = 0.375。

Some fractions produce terminating decimals, such as 1/4 = 0.25. Others produce repeating decimals, such as 1/3 = 0.333…, often written with a dot or bar over the repeating digit.

有些分数会得到有限小数，例如 1/4 = 0.25。有些则得到循环小数，例如 1/3 = 0.333…，通常用点或横线标出重复数字。

It is useful to memorise the most common fraction-decimal equivalences. They appear frequently in non-calculator papers and help you check your answers quickly.

记住最常见的分数与小数等价关系是很有用的。它们经常出现在非计算器试卷中，可以帮助你快速检查答案。

• 1/2 = 0.5
  1/2 = 0.5
• 1/4 = 0.25 and 3/4 = 0.75
  1/4 = 0.25，3/4 = 0.75
• 1/5 = 0.2 and 1/8 = 0.125
  1/5 = 0.2，1/8 = 0.125
• 1/10 = 0.1 and 1/20 = 0.05
  1/10 = 0.1，1/20 = 0.05

3. Converting Decimals to Percentages | 小数转百分比

To convert a decimal to a percentage, multiply by 100 and add the percent symbol. This is the same as moving the decimal point two places to the right.

要把小数转换为百分比，乘以 100 并加上百分号。这相当于把小数点向右移动两位。

For example, 0.45 × 100 = 45%, 1.2 × 100 = 120%, and 0.035 × 100 = 3.5%. Percentages can be greater than 100% when the quantity is more than the original whole.

例如，0.45 × 100 = 45%，1.2 × 100 = 120%，0.035 × 100 = 3.5%。当数量超过原本的整体时，百分比可以大于 100%。

When a decimal has fewer than two decimal places, you can add zeros as placeholders before multiplying. For example, 0.7 = 0.70 = 70%.

当小数的位数不足两位时，可以在乘法前补零占位。例如，0.7 = 0.70 = 70%。

4. Converting Percentages to Fractions and Decimals | 百分比转分数和小数

To convert a percentage to a decimal, divide by 100. For example, 65% = 65 ÷ 100 = 0.65.

要把百分比转换为小数，除以 100。例如，65% = 65 ÷ 100 = 0.65。

To convert a percentage to a fraction, write it over 100 and simplify if possible. For example, 40% = 40/100 = 2/5.

要把百分比转换为分数，先写成以 100 为分母的分数，然后尽可能约分。例如，40% = 40/100 = 2/5。

If the percentage contains a decimal or fraction, multiply the numerator and denominator to clear it. For example, 12.5% = 12.5/100 = 125/1000 = 1/8.

如果百分比含有小数或分数，可以同时扩大分子和分母来消除。例如，12.5% = 12.5/100 = 125/1000 = 1/8。