Plates move about as fast as your fingernails grow: a few centimeters a year. That seems like nothing, but plates have been moving for hundreds of millions of years. To see what the motion adds up to, you need careful unit conversions.
| Unit | Equals |
|---|---|
| 1 m | 100 cm |
| 1 km | 1,000 m = 100,000 cm |
| 1 million years | 1,000,000 years |
Key idea
Distance = rate × time. A handy shortcut: 1 cm per year = 10 km per million years, because 1,000,000 cm = 10 km.
Why it works
Work in one set of units and the numbers take care of themselves. At 1 cm a year, a million years gives 1,000,000 cm. Divide by 100 to get 10,000 m, then by 1,000 to get 10 km. So 1 cm/yr is the same rate as 10 km per million years. Then 4 cm/yr is 40 km per million years, and in 50 million years that is 2,000 km: enough to open a sea.
Worked example: Two million years
A plate moves 5 cm a year. How far does it move in 2 million years, in kilometers?
- $5 \times 2{,}000{,}000 = 10{,}000{,}000$ cm.
- $10{,}000{,}000 \div 100 = 100{,}000$ m, and $100{,}000 \div 1{,}000 = 100$ km.
- Shortcut check: 5 cm/yr = 50 km per million years, × 2 = 100 km.
Answer: 100 km
Worked example: How long to open an ocean?
Two continents drift apart at 3 cm a year. How long until they are 3,000 km apart?
- 3 cm/yr = 30 km per million years.
- $3{,}000 \div 30 = 100$ million years.
Answer: About 100 million years
Common mistake
Losing track of units: 5 cm a year for 2 million years is 10 million centimeters, which is only 100 km, not 10 million km. Check: write the unit next to every number, and convert centimeters to kilometers (divide by 100,000) before you answer.