SI units.

Step 1 of 6

A number and a unit

To measure is to compare with a unit. When you say a table is 2 m long, you say it is $2$⁠ times as long as one metre. Without the unit the number says nothing: $2$⁠ what? Metres, feet or paces?

So that everyone measures in the same units, science uses the International System of Units, the SI. It has seven base units, and three of them come up throughout mechanics:

• length: the metre, m
• mass: the kilogram, kg
• time: the second, s

The other four are the ampere (electric current), the kelvin (temperature), the mole (amount of substance) and the candela (brightness of light). Every other unit is built from them.

Step 2 of 6

Nanometres

The SI prefixes are short names for powers of $10$⁠. You met kilo, centi and milli in the Unit on ratio and scale. For very small and very large things there are more:

Prefix	Symbol	Times
giga	G	$10^9$⁠
mega	M	$10^6$⁠
kilo	k	$10^3$⁠
milli	m	$10^{-3}$⁠
micro	µ	$10^{-6}$⁠
nano	n	$10^{-9}$⁠

A nanometre, 1 nm, is $10^{-9}$⁠ metres, a billionth of a metre. The scene is now at DNA, two billionths of a metre wide.

Step 3 of 6

Micrometres

The scene has moved on to the next stop, the cell. A cell is a hundredth of a millimetre wide, 0.01 mm. For a size like that there is a handier unit: the micrometre, 1 µm, a millionth of a metre. A millimetre has $1000$⁠ micrometres, because $10^{-3} \div 10^{-6} = 10^3$$10^{-3} \div 10^{-6} =$$10^3$⁠.

Step 4 of 6

Gigametres

Very large things have prefixes too. The Sun is one million four hundred thousand kilometres across, $1.4 \times 10^6$⁠ kilometres. A gigametre, 1 Gm, is $10^9$⁠ metres. To get there, go first to metres, the base unit, and from there to gigametres.

Step 5 of 6

Derived units

Most units in physics are not base units but derived units, built from them. Speed is length divided by time, so its unit is metres per second, m/s. Area is length times length, m².

The scene has one of these too: Solar System clock is measured in days per second, how many days of orbit pass each second on the screen. Change it and watch the planets speed up.

Acceleration is the change in speed each second: by how many metres per second the speed grows every second.

Step 6 of 6

Checking by units

Units are also a way to check. Both sides of an equation must have the same units, and you can add or subtract only quantities of the same kind: metres to metres, seconds to seconds. When you put units in place of numbers, they behave like letters in algebra: they cancel when you divide and combine when you multiply.

If a formula you wrote comes out in seconds where it should give metres, it is wrong, before you have put in a single number.