← Measurement toolkit; position, distance, and displacement

Convert a prefixed unit to the base unit

You've already seen what kilo-, centi-, and milli- mean. Measurements arrive wearing prefixes, and you will often need the same measurement in the base unit.

A road sign reads 3.2 km. A map app wants that length in meters. kilo- means one thousand, so each of those kilometers is 1000 m. The meter is the smaller unit, so the number of them is bigger: multiply. 3.2 × 1000 = 3200. The sign marks a 3200 m road.

Going back the other way, divide: a 5000 m ridge walk is 5000 ÷ 1000 = 5 km.

centi- works the same way with 100: 12 cm is 12 ÷ 100 = 0.12 m, and 0.3 m is 0.3 × 100 = 30 cm. milli- works the same way with 1000: 8 mm is 8 ÷ 1000 = 0.008 m, and 2 m is 2 × 1000 = 2000 mm.

Two numbers do all the work: 1000 for kilo- and milli-, 100 for centi-. Multiply going to the smaller unit; divide going to the bigger one.

Either way, the measurement itself never changes. Only the way it is written changes: the number and its unit together.

A hiking trail is 2.4 km long. How long is the trail in meters?

Write down the values in the question:

2.4 km, wanted in m

Write down the fact:

kilo- means × 1000

Meters are the smaller unit, so the number gets bigger. Multiply:

2.4 × 1000 = 2400

The trail is 2400 m long.

A trail marker reads 5.8 km. How far is that in meters?

A touchscreen responds in 250 ms. How long is that in seconds?

A camera flash lasts 8 ms. How long is the flash in seconds?

Write down the values in the question:

8 ms, wanted in s

Write down the fact:

milli- means ÷ 1000 going back to the base unit

Seconds are the bigger unit, so the number gets smaller. Divide:

8 ÷ 1000 = 0.008

The flash lasts 0.008 s.

A pencil is 19 cm long. How long is the pencil in meters?

Your turn

A running track's straight section is 400 m. How long is that section in kilometers?

One heartbeat lasts 0.8 s. How long is that in milliseconds?

A desk is 0.75 m wide. How wide is the desk in centimeters?