📚 Fractions, Decimals and Percentages with 0.73 | 从0.73看分数、小数与百分比
Welcome to this IGCSE Edexcel Mathematics revision guide. In this article, we focus on a key number skill: converting between fractions, decimals and percentages. By using 0.73 as our starting point, you will see how straightforward these conversions can be when you grasp the underlying place value and proportional reasoning.
欢迎来到本篇IGCSE Edexcel数学复习指南。本文聚焦一个关键的数字技能：分数、小数和百分比之间的相互转换。以0.73为出发点，你会发现，只要掌握了潜在的位值和比例推理，这些转换其实非常简单直接。
The number 0.73 is a terminating decimal that can represent a fraction of a whole, a percentage, or a proportion. Mastering its conversions will build a strong foundation for more complex topics like percentage change, recurring decimals, and algebraic fractions.
数字0.73是一个有限小数，它可以表示整体的一部分、一个百分数或一个比例。掌握它的转换将为你学习更复杂的主题（如百分比变化、循环小数和代数分数）打下坚实的基础。
1. Understanding the Decimal 0.73 | 理解小数 0.73
hundredths place, meaning 3 × 1/100 = 3/100. Together, 0.73 equals 7/10 + 3/100 = 73/100.
在十进制数系统中，小数点后的每个数字都基于10的幂次具有不同的位值。第一位是十分位（1/10），第二位是百分位（1/100），依此类推。在0.73中，数字7在十分位上，表示7 × 1/10 = 7/10，数字3在百分位上，表示3 × 1/100 = 3/100。合起来，0.73 等于 7/10 + 3/100 = 73/100。
This place value understanding is crucial because it allows you to instantly write any terminating decimal as a fraction with a denominator that is a power of 10.
这种对位值的理解至关重要，因为它能让你瞬间将任何有限小数化为分母为10的幂次的分数。
2. Converting a Decimal to a Fraction | 小数化分数
The numerator is simply the digits after the decimal point: 73. Therefore, 0.73 = 73/100.
将有限小数化为分数，数一数小数部分有几位。0.73有两位小数，所以分母是 10² = 100。分子就是小数点后的数字：73。因此，0.73 = 73/100。
Let' f you have 0.073, the three decimal places give a denominator of 1000, so 0.073 = 73/1000.
让我们将这个规则应用到更多例子：0.5有一位小数，所以 0.5 = 5/10（可化简为1/2）。0.25有两位小数，所以 0.25 = 25/100 = 1/4。如果是0.073，三位小数意味着分母为1000，因此 0.073 = 73/1000。
3. From Fraction to Percentage | 分数与百分数的转换
A percentage is simply a fraction with a denominator of 100. The symbol % means 'out of 100'. To convert any fraction to a percentage, multiply by 100%. For the fraction 73/100, this is straightforward: 73/100 × 100% = 73%.
百分数本质上是一个分母为100的分数。符号 % 表示“每百”。要将任何分数转换为百分数，只需乘以100%。对于分数73/100，这很直接：73/100 × 100% = 73%。
ivide the numerator by the denominator and multiply by 100. For example, 3/5 = 60/100 = 60%. Alternatively, 3 ÷ 5 = 0.6, and 0.6 × 100 = 60%.
当分母不是100时，你可以先找到一个等价分数使其分母为100，或者直接用分子除以分母再乘以100。例如，3/5 = 60/100 = 60%。或者，3 ÷ 5 = 0.6，0.6 × 100 = 60%。
Percentage = (Numerator ÷ Denominator) × 100%
百分数 = (分子 ÷ 分母) × 100%
4. Simplifying Fractions: Is 73/100 in its Simplest Form? | 分数化简：73/100是最简分数吗？
To simplify a fraction, find the highest common factor (HCF) of the numerator and denominator and divide both by it. The number 73 is a prime number, and its factors are only 1 and 73. Since 73 does not divide 100, the HCF of 73 and 100 is 1. Therefore, 73/100 is already in its simplest form.
化简分数时，要找出分子和分母的最大公因数（HCF），并用它去约分。数字73是一个质数，它的因数只有1和73。由于73不能整除100，所以73和100的最大公因数是1。因此，73/100已经是最简分数。
00. The HCF of 75 and 100 is 25. Dividing numerator and denominator by 25 gives 3/4. Always check if your fraction can be simplified, especially in IGCSE exams where marks are awarded for writing answers in simplest form.
对比一下0.75这个例子。写成分数，0.75 = 75/100。75和100的最大公因数是25。分子分母同除以25得到3/4。一定要检查你的分数是否可以化简，特别是在IGCSE考试中，答案写成最简分数才能得满分。
5. Decimal ↔ Percentage Conversions | 小数与百分数互化
Converting a decimal to a percentage is simply multiplying by 100. This is equivalent to moving the decimal point two places to the right. For 0.73, moving the point two places gives 73%. If there are not enough digits, add zeros. For example, 0.073 becomes 7.3%, and 0.7 becomes 70%.
将小数转换为百分数就是乘以100，相当于把小数点向右移动两位。对0.73，小数点右移两位得到73%。如果位数不够就补零。例如，0.073变成7.3%，0.7变成70%。
To convert a percentage back to a decimal, divide by 100, which moves the decimal point two places to the left. 73% becomes 0.73, 7.3% becomes 0.073, and 170% becomes 1.70 or 1.7.
将百分数转换回小数，则要除以100，小数点向左移动两位。73%变成0.73，7.3%变成0.073，170%变成1.70或1.7。
| Decimal 小数 | Fraction 分数 | Percentage 百分数 |
|---|---|---|
| 0.73 | 73/100 | 73% |
| 0.5 | ½ | 50% |
| 0.25 | ¼ | 25% |
| 0.2 | ⅕ | 20% |
6. Ordering and Comparing Numbers | 数字排序与比较
A common IGCSE exam question asks you to order a mix of fractions, decimals and percentages. The safest method is to convert all numbers into the same form – usually decimals – and then compare. Let's order 0.73, 7/10, 70%, and 3/4 from smallest to largest.
IGCSE考试中常见的一类题目是要求将分数、小数和百分比混合排序。最稳妥的方法是把所有数字都转换成同一种形式——通常是小数——然后进行比较。我们来把0.73、7/10、70%和3/4从小到大排序。
Convert each: 0.73 is already a decimal. 7/10 = 0.7. 70% 7, 0.7, 0.75. The correct order from smallest to largest is 0.7 (which is both 7/10 and 70%), then 0.73, then 0.75 (3/4).
分别转换：0.73已经是小数。7/10 = 0.7。70% = 0.70（即0.7）。3/4 = 0.75。现在我们得到小数0.73、0.7、0.7、0.75。从小到大的正确顺序是0.7（即7/10和70%）、然后是0.73、最后是0.75（3/4）。
Always write down the original forms in the final answer as required. In this case, the order is: 7/10 and 70% (equal), 0.73, 3/4.
最终答案一定要按题目要求写出原来的数字形式。这里的顺序是：7/10和70%（相等）、0.73、3/4。
7. Recurring Decimals and Fractions | 循环小数与分数
So far we have worked with terminating decimals. However, some decimals, like 0.737373..., repeat forever. This is a recurring decimal and is written with dots above the repeating block: 0.7̇3̇. The block '73' repeats indefinitely, so it can be expressed as a fraction using an algebraic method.
到目前为止我们处理的都是有限小数。但有些小数，如0.737373...，会一直重复下去。这是一个循环小数，在重复的数字上方加点表示：0.7̇3̇。循环节“73”无限重复，因此可以用代数方法将它化成分数。
Let x = 0.7̇3&# 100x - x = 73.737373... - 0.737373... This gives 99x = 73. Solving for x gives x = 73/99.
设 x = 0.7̇3
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