Measurement
Metric Units & Conversion
From millimeters to kilometers, every conversion is just multiplying or dividing by a power of ten.
A textbook is about 26 centimeters, a building might be 30 meters, the next city is 200 kilometers away. All length — so why three units? Because metric units form a ladder: pick the right rung and the numbers stay readable. And the ladder has a beautiful property — every conversion on it is just multiplying or dividing by a power of ten.
One trick lets you move freely between millimeters, centimeters, meters and kilometers. Mass works the same way: milligrams, grams, kilograms.
A ladder built on tens
Length, from short to long:
| Unit | Relation |
|---|---|
| 1 kilometer | = 1000 meters |
| 1 meter | = 100 centimeters |
| 1 centimeter | = 10 millimeters |
Neighboring rungs are not always a factor of 10 apart, but the gaps are all powers of ten: mm→cm ×10, cm→m ×100, m→km ×1000. Mass is even tidier: mg→g→kg, every jump ×1000.
Chain the relations and you get longer leaps: 1 km = 100000 cm, 1 kg = 1000000 mg. Numbers that big are exactly why we usually pick the rung that fits the thing we measure.
Conversion is sliding the decimal point
Powers of ten have a wonderful property: to multiply or divide, you only slide the decimal point — no long multiplication needed.
- Big unit → small unit means multiply: km = m, the point moves three places right;
- Small unit → big unit means divide: cm = m, the point moves two places left.
Sliding works this smoothly thanks to place value: every position is worth a power of ten.
How to use
Common trap
"5 m 3 cm" is not m. Since 3 cm = m, the correct value is m — while m actually means 5 m 30 cm. This bites hardest when the centimeter part has a single digit.
Temperature: three different rulers
Temperature has units too, but they are not decimal — sliding the point does not work here:
- Celsius (°C): water freezes at 0 °C and boils at 100 °C, used by most of the world;
- Fahrenheit (°F): water freezes at 32 °F and boils at 212 °F, still common in the US. Converting takes a multiply and an add: , so a body temperature of 37 °C is about 98.6 °F;
- Kelvin (K): the scientists' choice. , and 0 K — absolute zero, about −273.15 °C — is the coldest anything can ever be.
When units go wrong
Units are not decoration. In 1999, NASA lost the Mars Climate Orbiter: two teams read the same thrust data in different unit systems, and the numbers were off by a factor of 4.45. A spacecraft worth over 300 million dollars was defeated by a unit mix-up.
Conversions also show up daily — pacing a run, or turning kilometers per hour into meters per second in Speed & Motion all use this same point-sliding skill.
Try it: how heavy is an elephant?
An Asian elephant weighs about 4.2 tonnes, and 1 tonne = 1000 kg, so it weighs kg. A sparrow at about 30 g comes to kg — the point slides three places left.
Check yourself
Quick quiz
1. 2.6 km equals how many meters?
2. 350 cm equals how many meters?
3. Body temperature is about 37 °C. What is that in Fahrenheit, roughly?