📚 Converting Fractions, Decimals and Percentages | 分数、小数和百分数的转换
Fractions, decimals and percentages are three different ways of expressing the same idea: a part of a whole. In everyday life, we see percentages in sale discounts, fractions in recipe measurements, and decimals in money and sports statistics. Mastering how to switch between these forms is a key skill in the Cambridge KS3 mathematics curriculum. This article will guide you through the core methods, common conversions, and practical uses of these three number forms.
分数、小数和百分数是表示“整体的一部分”这一相同概念的三种不同形式。在日常生活中，我们可以看到折扣用百分数表示，食谱用量用分数表示，而钱和体育统计数据都用小数表示。熟练掌握这些形式之间的转换是剑桥KS3数学课程中的一项关键技能。本文将引导你深入了解这三种数字形式的核心转换方法、常见换算以及实际应用。
1. Understanding the Basics | 理解基本概念
A fraction has a numerator (top number) and a denominator (bottom number). A decimal uses a decimal point and place value, while a percentage is a number out of 100. These three forms are equivalent representations of the same quantity. For example, half of a pizza can be written as 1/2, 0.5, or 50%.
分数有分子（上面的数字）和分母（下面的数字）。小数使用小数点及其位值，而百分数表示一个数是100的多少倍。这三种形式是同一个量的等价表示。例如，半个披萨可以写作1/2、0.5或50%。
The link between them comes from the idea of hundredths: a percentage is simply a fraction with denominator 100 written in a special way, and any decimal can be expressed as a fraction with a power of 10 in the denominator. Understanding this relationship makes conversion much easier.
它们之间的联系来自“百分之几”这一概念：百分数就是以100为分母的分数的一种特殊写法，而任何小数都可以表示成分母为10的幂次的分数。理解这一关系会让转换变得容易得多。
2. Converting Fractions to Decimals | 分数转换为小数
To turn a fraction into a decimal, divide the numerator by the denominator. You can use short division or long division depending on the numbers. For example, to convert 3/8 to a decimal, calculate 3 ÷ 8 = 0.375. If the denominator is a factor of 10, 100, or 1000, you can find an equivalent fraction with a denominator that is a power of ten and then write it as a decimal directly.
要把分数转换为小数，用分子除以分母。根据数字的不同，可以用短除法或长除法。例如，要将3/8转换为小数，计算3 ÷ 8 = 0.375。如果分母是10、100或1000的因数，可以先找到一个等值分数，使其分母为10的幂，然后直接写成小数。
For fractions like 1/4, multiply the numerator and denominator by 25 to get 25/100, which is 0.25. For 3/5, multiply by 2 to get 6/10, which gives 0.6. Always check if you can simplify the fraction before converting to avoid large numbers.
对于像1/4这样的分数，将分子和分母同时乘25得到25/100，即0.25。对于3/5，乘2得到6/10，即0.6。在转换前，先检查能否约简分数，以避免数字过大。
3. Converting Decimals to Fractions | 小数转换为分数
Write the decimal as a fraction with a denominator that is a power of 10, then simplify. The number of decimal places tells the power of 10: one decimal place gives tenths (denominator 10), two decimal places gives hundredths (100), three gives thousandths (1000), and so on. For example, 0.7 becomes 7/10, 0.25 becomes 25/100, which simplifies to 1/4.
将小数写成分母为10的幂的分数，然后约简。小数的位数决定了10的幂次：一位小数是十分之几（分母为10），两位小数是百分之几（100），三位小数是千分之几（1000），依此类推。例如，0.7变成7/10，0.25变成25/100，约简后得到1/4。
When there is a whole number part, keep it separate and only convert the decimal part to a fraction. For example, 4.2 becomes 4 + 2/10, which simplifies to 4 1/5. For recurring decimals, you need a different method, but at KS3 level, the focus is on terminating decimals.
当有整数部分时，将其保留，只将小数部分转换为分数。例如，4.2变成4 + 2/10，约简为4 1/5。对于循环小数，需要用另一种方法，不过在KS3阶段，重点在有限小数。
4. Converting Decimals to Percentages | 小数转换为百分数
Multiplying a decimal by 100 gives the percentage. This is because percent means ‘out of 100’. Simply move the decimal point two places to the right and add the % sign. For instance, 0.45 × 100 = 45%, and 0.08 becomes 8%. If the decimal has more digits, move the point two places as usual; for example, 0.625 × 100 = 62.5%.
将小数乘100就得到百分数。这是因为percent的意思是“每百分之”。只需将小数点向右移动两位，再加上%号。例如，0.45 × 100 = 45%，而0.08变为8%。如果小数位数较多，同样移动两位小数点；例如，0.625 × 100 = 62.5%。
When the decimal is greater than 1, the percentage will be greater than 100%. For example, 1.3 × 100 = 130%. This simply means the quantity is 130 parts out of 100, which is possible when we talk about increases.
当小数大于1时，百分数将大于100%。例如，1.3 × 100 = 130%。这表示该数量是100份中的130份，在谈论增长时是完全可能的。
5. Converting Percentages to Decimals | 百分数转换为小数
To change a percentage back to a decimal, divide by 100. This means moving the decimal point two places to the left. For example, 67% becomes 0.67, 5% becomes 0.05, and 120% becomes 1.2. When the percentage includes a fractional part, like 12.5%, write it as 12.5 ÷ 100 = 0.125.
要将百分数变回小数，除以100即可。这意味着将小数点向左移动两位。例如，67%变为0.67，5%变为0.05，120%变为1.2。当百分数包含小数部分时，如12.5%，写作12.5 ÷ 100 = 0.125。
Remember that percentages like 0.5% need careful attention: 0.5% = 0.5 ÷ 100 = 0.005. It is common to mistake this as 0.5, so always think about the size of the number.
要记住，像0.5%这样的百分数需要小心：0.5% = 0.5 ÷ 100 = 0.005。人们常常把它错当成0.5，所以一定要思考数值的大小。
6. Converting Fractions to Percentages | 分数转换为百分数
One reliable method is first to convert the fraction to a decimal by dividing, and then multiply the decimal by 100 to obtain the percentage. For example, 3/8 = 0.375, and 0.375 × 100 = 37.5%. Alternatively, you can find an equivalent fraction with a denominator of 100. So 3/8 is equivalent to 37.5/100, giving 37.5%.
一种可靠的方法是先将分数化为小数（用除法），再将小数乘100得到百分数。例如，3/8 = 0.375，然后0.375 × 100 = 37.5%。另一种方法是找到一个分母为100的等值分数。所以3/8可以化成37.5/100，即37.5%。
When the denominator is a factor of 100, this method is very quick. For instance, 7/25 = (7 × 4) / (25 × 4) = 28/100 = 28%. Practise spotting denominators like 2, 4, 5, 10, 20, 25, 50 that easily become 100.
当分母是100的因数时，这种方法非常快。例如，7/25 = (7×4)/(25×4) = 28/100 = 28%。要练习识别像2、4、5、10、20、25、50这样容易变成100的分母。
7. Converting Percentages to Fractions | 百分数转换为分数
Write the percentage as a fraction with denominator 100, then simplify if possible. For example, 40% = 40/100, which simplifies to 2/5. If the percentage includes a decimal, like 22.5%, first write it as 22.5/100, then multiply numerator and denominator by 10 to clear the decimal: 225/1000, and simplify to 9/40.
将百分数写成分母为100的分数，然后尽可能约简。例如，40% = 40/100，约简为2/5。如果百分数包含小数，如22.5%，先写成22.5/100，然后将分子分母同乘10以消除小数：225/1000，再约简为9/40。
Always write the fraction in its simplest form unless the question says otherwise. For mixed-number percentages such as 112 1/2%, convert the fractional part separately: 1/2% = 0.5%, so 112 1/2% = 112.5%, then write as 112.5/100 = 1125/1000 = 9/8.
除非题目另有要求，否则总是将分数写成最简形式。对于带分数百分数，如112 1/2%，分别处理分数部分：1/2% = 0.5%，所以112 1/2% = 112.5%，然后写成112.5/100 = 1125/1000 = 9/8。
8. Common Conversions to Memorise | 需要记住的常见转换
Knowing a few key equivalences by heart greatly speeds up problem-solving. The table below shows the most frequently used fractions, decimals and percentages in KS3 mathematics.
熟记一些关键的等价关系能大大加快解题速度。下表列出了KS3数学中最常用的分数、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… | 33 1/3% |
| 2/3 | 0.666… | 66 2/3% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
These common equivalents appear again and again in tests and real-life situations. Regular practice with flashcards or quick quizzes helps fix them in memory.
这些常见的等价关系在考试和实际情景中反复出现。用抽认卡或快速小测验进行经常性练习，有助于把它们记牢。
9. Applications in Real Life | 实际生活中的应用
When shopping, a ‘20% off’ label means you need to find 20% of the original price. If the item costs £45, then 20% = 0.2 × 45 = £9 discount. The sale price is £36. Similarly, test scores are often given as percentages, e.g. 32 out of 40 = 32/40 = 4/5 = 0.8 = 80%.
购物时，“八折”标签意味着你要算出原价的20%。如果商品标价45英镑，那么20% = 0.2 × 45 = 9英镑的折扣，到手价为36英镑。同样，测验分数常以百分数表示，如40分中的32分 = 32/40 = 4/5 = 0.8 = 80%。
Recipes may require 3/4 of a cup of sugar, but measuring jugs often show decimal markings. Converting between fractions and decimals helps you measure accurately. In finance, an interest rate of 3.5% is used in decimal form (0.035) for calculations.
食谱可能需要3/4杯糖，但量杯通常标的是小数刻度。学会在分数和小数间转换能让你精确量取。在金融领域，3.5%的利率在计算中需要以小数形式(0.035)出现。
10. Practice Problems and Tips | 练习题与技巧
Try converting the following to build confidence: (a) Write 7/8 as a decimal and a percentage. (b) Express 0.72 as a fraction in simplest form. (c) A test score is 68%. What is this as a fraction and a decimal? Answers: (a) 0.875 and 87.5%; (b) 18/25; (c) 17/25 and 0.68.
尝试进行下列转换以建立信心：(a) 把7/8写成小数和百分数。(b) 将0.72化为最简分数。(c) 某测验得分为68%，请写成分数和小数。答案：(a) 0.875和87.5%；(b) 18/25；(c) 17/25和0.68。
A common mistake is forgetting to simplify fractions completely. Always check if the numerator and denominator share a common factor greater than 1. Another tip is to use the decimal division method when the denominator is not a factor of 100, as it always works. And never move the decimal point in the wrong direction when switching between percentages and decimals — double-check your answer makes sense.
一个常见的错误是忘记把分数约简单到最简形式。永远要检查分子和分母是否有大于1的公因数。另一个技巧是，当分母不是100的因数时，用除法的十进制转换方法，因为它总能奏效。另外，在百分数和小数间转换时，不要将小数点移错方向——记得复查答案是否合理。
Using the fact that 100% represents a whole, any percentage less than 100% corresponds to a number less than 1, and any percentage greater than 100% gives a number larger than 1. This simple check can help you catch many errors.
利用“100%代表整体”这一事实，任何小于100%的百分数都对应一个小于1的数字，任何大于100%的百分数都给出一个大于1的数。这个简单的检验可以帮助你发现很多错误。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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