Converting between Units of Length | 长度单位换算

📚 Converting between Units of Length | 长度单位换算

Length is one of the most fundamental quantities we measure every day, from the height of a classroom door to the distance between two cities. In IGCSE Mathematics, you must be able to convert confidently between different units of length, both within the metric system and between metric and imperial systems.

长度是我们日常生活中最基础的测量量之一，从教室门的高度到两座城市之间的距离。在 IGCSE 数学中，你必须能够熟练地在不同长度单位之间进行换算，既包括公制系统内部的换算，也包括公制与英制系统之间的换算。

1. The Metric System | 公制系统

The metric system is a decimal-based system of measurement, meaning that each unit differs from the next by a power of 10. The base unit of length in the metric system is the metre (m).

公制系统是一种基于十进制的测量系统，意味着每个单位与相邻单位相差 10 的幂次。公制系统中长度的基本单位是米（m）。

The most common metric units of length are:

最常见的公制长度单位有：

Kilometre (km) — 千米（公里）
Metre (m) — 米
Centimetre (cm) — 厘米
Millimetre (mm) — 毫米

The prefixes tell you the relationship to the base unit. ‘Kilo-‘ means 1000 times, ‘centi-‘ means one hundredth, and ‘milli-‘ means one thousandth.

前缀告诉你与基本单位之间的关系。”千”（kilo-）表示 1000 倍，”厘”（centi-）表示百分之一，”毫”（milli-）表示千分之一。

2. Converting within the Metric System | 公制系统内部的换算

Because the metric system is based on powers of 10, converting between units simply involves multiplying or dividing by 10, 100, or 1000.

由于公制系统基于十的幂次，单位之间的换算只需乘以或除以 10、100 或 1000。

The key relationships you must memorise are:

你必须记住的关键关系有：

1 km = 1000 m | 1 m = 100 cm | 1 m = 1000 mm | 1 cm = 10 mm

To convert from a larger unit to a smaller unit, multiply. To convert from a smaller unit to a larger unit, divide.

从较大单位换算到较小单位时，乘以进率。从较小单位换算到较大单位时，除以进率。

Example 1: Convert 3.5 km to metres.

例 1：将 3.5 千米换算为米。

3.5 × 1000 = 3500 m

Since we are going from kilometres to metres, we multiply by 1000 because 1 km = 1000 m.

因为从千米到米，进率为 1000，所以乘以 1000。

Example 2: Convert 250 mm to centimetres.

例 2：将 250 毫米换算为厘米。

250 ÷ 10 = 25 cm

Here we divide by 10 because 1 cm = 10 mm, so each centimetre contains 10 millimetres.

这里除以 10，因为 1 厘米 = 10 毫米，每一厘米包含 10 毫米。

Conversion \| 换算	Operation \| 运算	Example \| 示例
km → m	× 1000	2.4 km = 2400 m
m → cm	× 100	1.8 m = 180 cm
cm → mm	× 10	7.5 cm = 75 mm
m → mm	× 1000	0.62 m = 620 mm
mm → cm	÷ 10	450 mm = 45 cm
cm → m	÷ 100	320 cm = 3.2 m
m → km	÷ 1000	5400 m = 5.4 km

3. Converting Multiple Steps | 多步换算

Sometimes you need to convert through an intermediate unit. For example, converting millimetres to metres requires going through centimetres.

有时你需要通过中间单位进行换算。例如，将毫米换算为米需要经过厘米。

Example 3: Convert 4800 mm to metres.

例 3：将 4800 毫米换算为米。

Method 1: Convert step by step.

方法一：逐步换算。

4800 mm ÷ 10 = 480 cm then 480 cm ÷ 100 = 4.8 m

Method 2: Divide directly by the total factor. Since 1 m = 1000 mm, we divide by 1000.

方法二：直接除以总进率。因为 1 米 = 1000 毫米，直接除以 1000。

4800 ÷ 1000 = 4.8 m

When you are comfortable with the relationships, the direct method is faster. However, the step-by-step method is less prone to error, so use it when you are unsure.

当你熟悉了单位之间的关系后，直接法更快。然而，逐步法更不容易出错，所以在不确定时使用逐步法。

4. Imperial Units of Length | 英制长度单位

The imperial system is still used in some countries, including the United States and, partially, the United Kingdom. You should be familiar with inches, feet, yards, and miles.

英制系统仍被一些国家使用，包括美国和部分英国地区。你应该熟悉英寸、英尺、码和英里。

The relationships within the imperial system are:

英制系统内部的关系为：

1 foot (ft) = 12 inches (in) | 1 yard (yd) = 3 feet | 1 mile = 1760 yards = 5280 feet

Example 4: Convert 6 feet to inches.

例 4：将 6 英尺换算为英寸。

6 × 12 = 72 inches

Example 5: Convert 4.5 yards to feet.

例 5：将 4.5 码换算为英尺。

4.5 × 3 = 13.5 feet

Notice that imperial conversions use multiplication factors that are not powers of 10, which is exactly why the metric system is generally easier to work with in mathematics.

注意英制换算使用的乘数不是 10 的幂次，这正是为什么在数学中公制系统通常更容易使用。

5. Key Conversion Factors Between Systems | 公制与英制之间的关键换算因子

For IGCSE Edexcel, you will often be given the conversion factor in the exam question, but you should memorise the most common ones to save time.

对于 IGCSE Edexcel 考试，题目通常会给出换算因子，但你应该记住最常见的几个以节省时间。

The most important conversions to memorise are:

最重要的需要记住的换算有：

1 inch = 2.54 cm | 1 foot = 30.48 cm | 1 mile ≈ 1.609 km

Approximately, you can also use:

近似地，你还可以使用：

1 m ≈ 3.28 feet | 1 km ≈ 0.621 miles

These approximate values are useful for quick mental calculations and for checking whether your answer is reasonable.

这些近似值对于快速心算和检查答案是否合理非常有用。

6. Converting from Metric to Imperial | 公制换算为英制

To convert from a metric unit to an imperial unit, you multiply or divide by the appropriate conversion factor.

要将公制单位换算为英制单位，你需要乘以或除以相应的换算因子。

Example 6: A pencil is 15 cm long. Convert this length to inches.

例 6：一支铅笔长 15 厘米。将这个长度换算为英寸。

Since 1 inch = 2.54 cm, we divide the length in centimetres by 2.54.

因为 1 英寸 = 2.54 厘米，我们将厘米数除以 2.54。

15 ÷ 2.54 ≈ 5.91 inches

Example 7: A running track is 400 m long. Convert this to feet.

例 7：一条跑道长 400 米。将其换算为英尺。

Using the conversion 1 m ≈ 3.28 feet:

使用换算关系 1 米 ≈ 3.28 英尺：

400 × 3.28 = 1312 feet

Example 8: A marathon is approximately 42.2 km. Convert this to miles.

例 8：马拉松约为 42.2 千米。将其换算为英里。

Using the conversion 1 km ≈ 0.621 miles:

使用换算关系 1 千米 ≈ 0.621 英里：

42.2 × 0.621 ≈ 26.2 miles

This matches the well-known fact that a marathon is about 26 miles.

这与众所周知的马拉松大约为 26 英里相符。

7. Converting from Imperial to Metric | 英制换算为公制

To convert from imperial units to metric units, flip the conversion factor. For example, since 1 inch = 2.54 cm, you multiply inches by 2.54 to get centimetres.

要将英制单位换算为公制单位，翻转换算因子即可。例如，因为 1 英寸 = 2.54 厘米，将英寸数乘以 2.54 就得到厘米数。

Example 9: A doorway is 6.5 feet tall. Convert this height to metres.

例 9：一扇门高 6.5 英尺。将这个高度换算为米。

First convert feet to centimetres, then centimetres to metres.

先将英尺换算为厘米，再将厘米换算为米。

6.5 × 30.48 = 198.12 cm then 198.12 ÷ 100 = 1.98 m

So the doorway is approximately 1.98 m tall.

所以这扇门大约高 1.98 米。

Example 10: The distance between two towns is 15 miles. Convert this to kilometres.

例 10：两个城镇之间的距离是 15 英里。将其换算为千米。

Since 1 mile ≈ 1.609 km:

因为 1 英里 ≈ 1.609 千米：

15 × 1.609 ≈ 24.1 km

Always check that your answer makes sense. Since a kilometre is shorter than a mile, the number of kilometres should be larger than the number of miles.

始终检查你的答案是否合理。因为 1 千米比 1 英里短，所以千米的数量应该大于英里的数量。

8. Real-World Applications | 实际应用

Unit conversion is not just an abstract exercise — it appears in real-world contexts such as construction, engineering, and travel.

单位换算不仅仅是抽象的练习——它出现在建筑、工程和旅行等现实情境中。

Example 11: A carpenter has a plank that is 2.4 m long. He needs to cut it into pieces of 15 cm each. How many full pieces can he cut?

例 11：一位木匠有一块长 2.4 米的木板。他需要将其切割成每段 15 厘米的小段。他最多能切出多少段完整的？

First, convert everything to the same unit. Convert 2.4 m to centimetres.

首先，将所有单位统一。将 2.4 米换算为厘米。

2.4 × 100 = 240 cm then 240 ÷ 15 = 16 pieces

The carpenter can cut 16 full pieces of 15 cm each.

木匠可以切出 16 段完整的 15 厘米小段。

Example 12: A map has a scale of 1 : 50,000. If two points on the map are 8 cm apart, what is the actual distance in kilometres?

例 12：一张地图的比例尺为 1 : 50,000。如果地图上两点相距 8 厘米，实际距离是多少千米？

Multiply the map distance by the scale factor.

将图上距离乘以比例因子。

8 × 50,000 = 400,000 cm

Now convert to metres, then to kilometres.

现在换算为米，再换算为千米。

400,000 ÷ 100 = 4000 m then 4000 ÷ 1000 = 4 km

The actual distance is 4 km.

实际距离为 4 千米。

9. Common Mistakes and Tips | 常见错误与技巧

Students often make predictable errors when converting units. Here are the most common pitfalls and how to avoid them.

学生在进行单位换算时经常犯一些可预见的错误。以下是最常见的陷阱以及如何避免它们。

Mistake: Multiplying when you should divide. Always ask yourself: ‘Am I going from a larger unit to a smaller unit, or from a smaller unit to a larger unit?’
错误：该除的时候乘了。始终问自己：”我是在从大单位换到小单位，还是从小单位换到大单位？”

Mistake: Forgetting to convert all values to the same unit before calculating. In any problem, always unify the units first.
错误：在计算前忘记将所有值转换为相同单位。在任何问题中，始终先统一单位。

Mistake: Using the wrong conversion factor. For example, confusing 1 m = 100 cm with 1 m = 1000 mm. Write down the conversion factor before you begin.
错误：使用错误的换算因子。例如，混淆 1 米 = 100 厘米和 1 米 = 1000 毫米。开始之前先写下换算因子。

Tip: Use a rough estimate to check your answer. For instance, if you convert 5 km to miles, you expect about 3 miles because 1 km is roughly 0.6 miles.
技巧：用粗略估算来检查答案。例如，将 5 千米换算为英里时，你预期大约为 3 英里，因为 1 千米大约是 0.6 英里。

Tip: Write ‘× factor’ or ‘÷ factor’ clearly in your working. Examiners award method marks for correct processes even if the final answer has a small error.
技巧：在解题过程中清晰地写出”× 进率”或”÷ 进率”。考官会根据正确的过程给方法分，即使最终答案有些小错误。

10. Practice Questions | 练习题

Try these questions on your own before checking the solutions below.

先尝试独立完成以下题目，再对照下面的解答。

Question 1: Convert 7.25 km to metres.

题目 1：将 7.25 千米换算为米。

Question 2: Convert 850 mm to centimetres.

题目 2：将 850 毫米换算为厘米。

Question 3: A table is 1.5 m long. Express this length in feet, given that 1 m ≈ 3.28 ft.

题目 3：一张桌子长 1.5 米。已知 1 米 ≈ 3.28 英尺，用英尺表示这个长度。

Question 4: A field is 120 yards long. Convert this to metres, given that 1 yard = 0.9144 m.

题目 4：一块田地长 120 码。已知 1 码 = 0.9144 米，将其换算为米。

Question 5: A piece of wire is 3 m 40 cm long. Write this length in centimetres.

题目 5：一段电线长 3 米 40 厘米。用厘米写出这个长度。

Solutions | 解答：

1) 7.25 × 1000 = 7250 m

2) 850 ÷ 10 = 85 cm

3) 1.5 × 3.28 = 4.92 ft

4) 120 × 0.9144 = 109.7 m (to 1 decimal place)

5) 3 m = 300 cm, so 300 + 40 = 340 cm

For question 5, remember to convert each part of the mixed unit separately, then add the results together.

对于题目 5，记得将混合单位的每一部分分别换算，然后将结果相加。

11. Exam Tips for Edexcel IGCSE | Edexcel IGCSE 考试技巧

In the Edexcel IGCSE Mathematics exam, unit conversion questions can appear in both Paper 1 and Paper 2. They may be standalone questions or embedded within larger problems involving area, volume, speed, or scale drawings.

在 Edexcel IGCSE 数学考试中，单位换算题可能出现在试卷一和试卷二中。它们可能是独立题目，也可能嵌入到涉及面积、体积、速度或比例尺的更大问题中。

Always read the question carefully to see which unit the answer should be given in. If the question asks for an answer in metres, do not leave your final answer in centimetres.

始终仔细阅读题目，看答案应该使用哪个单位。如果题目要求以米为单位作答，不要把最终答案留在厘米。

Pay attention to the accuracy required. Some questions specify ‘give your answer to 1 decimal place’ or ‘to the nearest whole number’. Follow these instructions precisely.

注意所需的精确度。有些题目要求”答案保留一位小数”或”精确到最接近的整数”。严格遵循这些要求。

Finally, remember that conversion factors are provided in the exam formula sheet when needed, but knowing the core metric conversions by heart will save you valuable time and reduce the risk of errors.

最后，记住在需要时考试公式表中会提供换算因子，但熟记核心公制换算可以节省宝贵的时间并减少出错的风险。

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Converting between Units of Length | 长度单位换算