Units of measure · 度量单位
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| metric/ˈmetrɪk/ | 公制 | gōng zhì |
| length/leŋθ/ | 长度 | cháng dù |
| mass/mæs/ | 质量 | zhì liàng |
| capacity/kəˈpæsɪti/ | 容量 | róng liàng |
The Mars orbiter that cost 125 million dollars
- In 1999, NASA lost the Mars Climate Orbiter because one team used metres and another used feet.
- Unit mistakes aren't just embarrassing — they can be catastrophic. Getting units right is a core mathematical skill.
Unit choice lab · 单位选择实验
Choose the unit that matches the measurement scale. · 选择与测量尺度相匹配的单位。
Metric 公制 length 长度, mass 质量 and capacity 容量
- Length: $10\text{ mm}=1\text{ cm}$, $100\text{ cm}=1\text{ m}$, $1000\text{ m}=1\text{ km}$. Moving to a larger unit divides the number.
- Mass: $1000\text{ g}=1\text{ kg}$. Divide by 1000 from g to kg; multiply from kg to g.
- Capacity: $1000\text{ ml}=1\text{ litre}$; $\;1\text{ litre} = 1000\text{ cm}^3$.
- $1\text{ m} = 100\text{ cm} = 1000\text{ mm}$.
$2.5\text{ kg} = 2500\text{ g}$. $350\text{ ml} = 0.35\text{ litres}$. Always multiply when going to a smaller unit, divide for a larger one.
Changing length units: multiply going down, divide going up
How many cm are there in 1 m? · 1 m 中有多少 cm？
1 m = 100 cm. · 1 m = 100 cm。
How many cm³ are there in 1 litre? · 1 升中有多少 cm³？
1 litre = 1000 cm³. · 1 升 = 1000 cm³。
Area and volume conversions need care
- Area conversions are squared: $1\text{ m}^2 = 100^2 = 10\,000\text{ cm}^2$.
- Volume conversions are cubed: $1\text{ m}^3 = 100^3 = 1\,000\,000\text{ cm}^3$.
Don't just multiply by 100. $3\text{ m}^2 = 30\,000\text{ cm}^2$, NOT $300\text{ cm}^2$. You must square the conversion factor: $3 \times 100^2 = 3 \times 10\,000$.
Convert 3 m² to cm². (1 m² = 10 000 cm²) · 将 3 m² 转换为 cm²。（1 m² = 10 000 cm²）
3 × 10 000 = 30 000 cm². · 3 × 10 000 = 30 000 cm²。
Convert 0.5 m³ to cm³. · 将 0.5 m³ 转换为 cm³。
0.5 × 1 000 000 = 500 000 cm³. · 0.5 × 1 000 000 = 500 000 cm³。
1 m² = 100 cm². · 1 m² = 100 cm²。
1 m² = 100² = 10 000 cm², not 100 cm². The conversion factor must be squared for area. · 1 m² = 100² = 10 000 cm²，而非 100 cm²。面积换算因子必须平方。
To convert m³ to cm³, multiply by ______. · 要将 m³ 转换为 cm³，需乘以 ______。
1 m³ = 100³ cm³ = 1 000 000 cm³. · 1 m³ = 100³ cm³ = 1 000 000 cm³。
Worked examples
- $3\text{ m}^2 = 3 \times 10\,000 = 30\,000\text{ cm}^2$.
- $0.5\text{ m}^3 = 0.5 \times 1\,000\,000 = 500\,000\text{ cm}^3$.
- $2\,500\text{ cm}^3 = 2.5\text{ litres}$ (divide by $1000$).
Fun fact
- The metre was originally defined as $\dfrac{1}{10\,000\,000}$ of the distance from the equator to the North Pole. It's now defined using the speed of light: $1\text{ m} =$ the distance light travels in $\dfrac{1}{299\,792\,458}$ seconds.
Converting units is about moving between scales on this number line — from millimetres to kilometres and beyond.
You've got it
- $1\text{ m} = 100\text{ cm}$, so $1\text{ m}^2 = 10\,000\text{ cm}^2$ and $1\text{ m}^3 = 1\,000\,000\text{ cm}^3$
- square the conversion for area, cube it for volume
- $1\text{ litre} = 1000\text{ cm}^3$; $\;1\text{ m}^3 = 1000\text{ litres}$