Fractions, Decimals and Percentages Conversion | 分数、小数与百分数的转换

📚 Fractions, Decimals and Percentages Conversion | 分数、小数与百分数的转换

Fractions, decimals and percentages are three different ways of representing parts of a whole. In Key Stage 3 mathematics, being able to switch confidently between these forms is an essential skill. Whether you are comparing test scores, calculating discounts or working with probability, you will need to convert fluently from one form to another. This article explains every conversion method step by step, with plenty of examples, to help you master the topic.

分数、小数和百分数是表示整体之部分的三种不同方式。在 KS3 数学中，能够自信地在这些形式之间切换是一项基本技能。无论你是在比较考试成绩、计算折扣，还是处理概率问题，都需要熟练地进行相互转换。本文将逐步讲解每一种转换方法，并提供大量示例，帮助你掌握这一主题。

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1. Understanding Fractions, Decimals and Percentages | 理解分数、小数和百分数

A fraction shows a part of a whole using a numerator and a denominator. For example, 3/4 means 3 parts out of 4 equal parts. A decimal uses a decimal point to show tenths, hundredths, thousandths and so on. For example, 0.75 represents 75 hundredths. A percentage is a special fraction with a denominator of 100; the symbol % means “out of 100”. So 75% literally means 75 per 100.

分数用分子和分母来表示整体的一部分。例如，3/4 表示 4 等份中的 3 份。小数用小数点来表示十分位、百分位、千分位等。例如，0.75 表示 75 个百分之一。百分数是一种特殊分数，分母为 100；符号 % 表示“每一百”。因此，75% 的字面意思就是每一百中的 75。

Because all three represent the same idea – a proportion – we can convert between them. The key is to remember that the fraction bar means division, and that multiplying a decimal by 100 gives the percentage.

因为这三者表达的是同一个概念——比例——所以我们可以互相转换。关键在于记住分数线表示除法，以及将小数乘以 100 就得到百分数。

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2. Converting Fractions to Decimals | 将分数转换为小数

To turn a fraction into a decimal, simply divide the numerator by the denominator. For a simple fraction like 1/2, do 1 ÷ 2 = 0.5. For 3/8, divide 3 by 8 to get 0.375. This works for proper fractions, improper fractions and mixed numbers.

要将分数转换为小数，只需用分子除以分母。对于像 1/2 这样的简单分数，计算 1 ÷ 2 = 0.5。对于 3/8，用 3 除以 8 得到 0.375。这一方法适用于真分数、假分数和带分数。

If the denominator is a power of 10 (10, 100, 1000), the conversion is even easier. For example, 7/10 = 0.7, 23/100 = 0.23, and 9/1000 = 0.009. You just need to write the numerator and place the decimal point so there are as many decimal places as zeros in the denominator.

如果分母是 10 的幂（10, 100, 1000），转换就更容易。例如，7/10 = 0.7，23/100 = 0.23，9/1000 = 0.009。你只需要写下分子，然后放置小数点，使小数位数等于分母中零的个数。

Some fractions produce recurring decimals, such as 1/3 = 0.333… and 2/11 = 0.181818… In KS3 work you can often round these to a given number of decimal places, but it is important to recognise that the decimal goes on forever.

有些分数会产生循环小数，例如 1/3 = 0.333…，2/11 = 0.181818…。在 KS3 学习中，你通常可以将它们四舍五入到指定的小数位数，但重要的是要认识到这个小数会无限循环下去。

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3. Converting Decimals to Fractions | 将小数转换为分数

To change a terminating decimal into a fraction, first identify the place value of the last digit. For example, 0.7 has the 7 in the tenths place, so write it as 7/10. 0.25 has the 5 in the hundredths place, so write 25/100 and then simplify to 1/4.

要将有限小数转换为分数，首先要确定最后一位数字的位值。例如，0.7 的 7 在十分位，因此写为 7/10。0.25 的 5 在百分位，因此写为 25/100，然后化简为 1/4。

If the decimal has a whole number part, separate it first. 3.8 can be thought of as 3 + 0.8. Turn 0.8 into 8/10 = 4/5, so the fraction is 3 4/5 or 19/5 as an improper fraction.

如果小数有整数部分，先把它分开处理。3.8 可以看作 3 + 0.8。将 0.8 转换为 8/10 = 4/5，因此分数为 3 4/5 或作为假分数 19/5。

Always simplify the fraction to its lowest terms by dividing numerator and denominator by their highest common factor. This makes answers neater and easier to compare.

始终将分数化简为最简形式，方法是用分子和分母的最大公因数进行约分。这样得出的答案更简洁，也更容易比较。

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4. Converting Decimals to Percentages | 将小数转换为百分数

To convert a decimal to a percentage, multiply it by 100 and add the % sign. This effectively moves the decimal point two places to the right. For example, 0.35 × 100 = 35%, and 0.08 × 100 = 8%.

将小数转换为百分数，乘以 100 并加上百分号。这实际上就是将小数点向右移动两位。例如，0.35 × 100 = 35%，0.08 × 100 = 8%。

If the decimal has more than two decimal places, the same rule applies. 0.125 × 100 = 12.5%, and 0.002 × 100 = 0.2%. You can also think of the decimal as hundredths: 0.2 is 2/10, which is the same as 20/100, so 20%.

如果小数有超过两位小数，规则同样适用。0.125 × 100 = 12.5%，0.002 × 100 = 0.2%。你也可以将小数看作百分位：0.2 是 2/10，等同于 20/100，所以是 20%。

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5. Converting Percentages to Decimals | 将百分数转换为小数

To change a percentage back to a decimal, divide by 100. This moves the decimal point two places to the left. For instance, 85% becomes 85 ÷ 100 = 0.85, and 4% becomes 4 ÷ 100 = 0.04. Remember to insert a zero in the tenths place if needed.

要将百分数转换回小数，除以 100。这相当于将小数点向左移动两位。例如，85% 变为 85 ÷ 100 = 0.85，4% 变为 4 ÷ 100 = 0.04。必要时记得在十分位补零。

For percentages that include a decimal themselves, such as 12.5%, simply divide by 100 to get 0.125. The process is exactly the same: move the decimal point two places left.

对于本身包含小数的百分数，例如 12.5%，只需除以 100 得到 0.125。过程完全一样：将小数点左移两位。

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6. Converting Fractions to Percentages | 将分数转换为百分数

There are two main methods to change a fraction to a percentage. The first method: convert the fraction to a decimal by dividing numerator by denominator, then multiply by 100. For 3/5, divide 3 by 5 to get 0.6, then 0.6 × 100 = 60%.

将分数转换为百分数有两种主要方法。第一种：先通过分子除以分母将分数化为小数，再乘以 100。对于 3/5，3 除以 5 得 0.6，然后 0.6 × 100 = 60%。

The second method works well when the denominator is a factor of 100. You can find an equivalent fraction with denominator 100. For 7/20, multiply numerator and denominator by 5: 7/20 = 35/100 = 35%. This is a very quick way if the numbers are friendly.

第二种方法在分母是 100 的因数时非常有效。你可以找到一个分母为 100 的等价分数。对于 7/20，将分子和分母同乘以 5：7/20 = 35/100 = 35%。如果数字比较友好，这是非常快捷的方法。

When the denominator does not divide into 100 neatly, the decimal method is more reliable. For example, 5/16 = 0.3125, so 31.25%.

当分母不能整除 100 时，小数法更可靠。例如，5/16 = 0.3125，因此为 31.25%。

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7. Converting Percentages to Fractions | 将百分数转换为分数

Write the percentage as a fraction with denominator 100, and then simplify if possible. For 30%, write 30/100, which simplifies to 3/10. For 125%, write 125/100 = 5/4 or 1 1/4.

将百分数写成分母为 100 的分数，然后尽可能化简。对于 30%，写作 30/100，化简为 3/10。对于 125%，写作 125/100 = 5/4 或 1 1/4。

If the percentage has a decimal part, like 12.5%, first eliminate the decimal by multiplying numerator and denominator by 10 or 100. 12.5% = 12.5/100 = 125/1000, which simplifies to 1/8. An easier route is to remember common equivalents, but always show your working.

如果百分数包含小数部分，如 12.5%，首先通过将分子分母同乘以 10 或 100 来消除小数。12.5% = 12.5/100 = 125/1000，化简为 1/8。更简单的方法是记住常见的等价关系，但一定要展示计算过程。

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8. Using 100% as a Reference | 以 100% 为参照

Understanding that 100% represents the whole is a powerful idea. If you know a fraction of the whole, subtract from 100% to find the remaining part. For example, if you have completed 3/8 of a task, the remaining fraction is 5/8, which is equivalent to 100% – 37.5% = 62.5%.

理解 100% 代表整体是一个强有力的概念。如果你知道整体的一个分数，从 100% 中减去它就能求出剩余的部分。例如，如果你已经完成了一项任务的 3/8，剩余的部分就是 5/8，相当于 100% – 37.5% = 62.5%。

You can also use 100% to frame fraction and percentage problems. If a price is reduced by 20%, the new price is 80% of the original. This makes percentage increase and decrease calculations much simpler when you work in decimals: decrease by 20% means multiply by 0.8.

你也可以利用 100% 来理解分数和百分数问题。如果价格降低了 20%，新价格是原价的 80%。当你使用小数进行计算时，这样会使百分比的增减运算简单得多：降低 20% 意味着乘以 0.8。

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9. Comparing and Ordering | 比较与排序

Often you need to compare a list of fractions, decimals and percentages. The safest method is to convert all values to the same form. Percentages or decimals are usually easiest because you can line up the numbers by place value.

你常常需要比较一列混合的分数、小数和百分数。最稳妥的方法是将所有数值转换为同一种形式。百分数或小数通常最容易，因为你可以按数位将数字对齐。

Example: put these in ascending order: 2/5, 0.45, 30%, 0.4. Convert 2/5 to 0.4, 30% to 0.3. Now the list becomes 0.4, 0.45, 0.3, 0.4. Clearly, 0.3 < 0.4 = 0.4 < 0.45, so the order is 30%, 2/5, 0.4, 0.45. Notice that 2/5 and 0.4 are equal.

示例：将下列各数按升序排列：2/5, 0.45, 30%, 0.4。将 2/5 转换为 0.4，30% 转换为 0.3。现在列表变为 0.4, 0.45, 0.3, 0.4。显然，0.3 < 0.4 = 0.4 < 0.45，因此顺序为 30%, 2/5, 0.4, 0.45。注意 2/5 和 0.4 是相等的。

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10. Quick Reference Table | 快速对照表

Memorising some common equivalents will speed up your work significantly. The table below shows fractions, decimals and percentages that appear very often in KS3 problems.

记住一些常见的等值关系能显著提高解题速度。下表列出了 KS3 题目中经常出现的分数、小数和百分数。

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/3	0.333… (0.33)	33.3%
2/3	0.666… (0.67)	66.7%
1/5	0.2	20%
2/5	0.4	40%
3/8	0.375	37.5%
1/8	0.125	12.5%

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11. Common Mistakes to Avoid | 常见错误与避坑

One frequent error is forgetting to simplify fractions fully. Always check if the numerator and denominator share a common factor after conversion. Another mistake is misplacing the decimal point when multiplying or dividing by 100; remember that multiplying by 100 moves the point right, and dividing moves it left.

一个常见错误是忘记将分数完全化简。转换之后，一定要检查分子和分母是否还有公因数。另一个错误是在乘以或除以 100 时点错小数点位置；记住乘以 100 是右移小数点，除以 100 是左移。

Some students confuse 0.5 with 5% or think that 1/3 equals 0.3 rather than 0.333… A solid understanding of place value and the meaning of the % symbol will help you avoid these slips.

有些学生会把 0.5 与 5% 混淆，或认为 1/3 等于 0.3 而不是 0.333…。扎实理解位值的概念和百分号的含义，有助于避免这些失误。

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12. Practice and Real-Life Applications | 练习与生活应用

Try converting the following: (a) 7/8 as a decimal and a percentage, (b) 0.65 as a fraction in simplest form, (c) 18% as a fraction and a decimal. Check your answers: (a) 0.875, 87.5%; (b) 13/20; (c) 9/50, 0.18. Regular practice builds fluency.

尝试转换下列各题：(a) 7/8 化为小数和百分数，(b) 0.65 化为最简分数，(c) 18% 化为分数和小数。检查答案：(a) 0.875, 87.5%; (b) 13/20; (c) 9/50, 0.18。经常练习能提高熟练度。

These skills are used in many real-world situations: calculating sale prices, reading survey results, mixing ingredients in recipes, and working with probability. The more you connect them to daily life, the more natural the conversions will feel.

这些技能在许多现实场景中都有应用：计算打折价格、阅读调查结果、按食谱配料混合、以及处理概率问题。你越多地将它们与日常生活联系起来，转换运用就会越自然。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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