1.1–1.4Units, prefixes and standard form
Every physical quantity has an SI unit, and marks are lost for leaving one off or getting one wrong far more often than for the physics itself. Learn the quantity and its unit as a pair, in both directions: given the unit, you should be able to name the quantity.
Prefixes are shorthand for a power of ten, and the same six come up over and over. Going up: kilo is a thousand, mega a million, giga a thousand million. Going down: centi is a hundredth, milli a thousandth, micro a millionth, nano a thousand millionth.
The rule for converting is worth stating once so you never guess. To go from a large unit to a small one, multiply; from a small unit to a large one, divide. 2.5 km is 2500 m because a kilometre is bigger than a metre; 40 mA is 0.040 A for the same reason in reverse.
Hours to seconds catches people out because it is two steps, not one: multiply by 60 for minutes, then by 60 again for seconds, so an hour is 3600 s. A speed given in km/h converted to m/s needs both changes at once — multiply by 1000 and divide by 3600, which is the same as dividing by 3.6.
Worked example
A car travels at 72 km/h. Express this speed in m/s. Give your answer in standard form to 2 significant figures.
- 72 km is 72 × 1000 = 72 000 m.
- One hour is 60 × 60 = 3600 s.
- Speed = 72 000 ÷ 3600 = 20 m/s.
- In standard form that is 2.0 × 10¹ m/s.
Answer: 20 m/s, or 2.0 × 10¹ m/s.
Standard form writes a number as a value between 1 and 10 multiplied by a power of ten. 0.00045 becomes 4.5 × 10⁻⁴; 380 000 becomes 3.8 × 10⁵. Count how many places the decimal point moves, and the direction gives the sign: left for a positive power, right for a negative one.
For significant figures, give an answer to the same number as the least precise measurement you were given. If a question supplies 2.5 m and 3.71 s, quote the answer to 2 significant figures. Do the rounding at the end, never in the middle of a multi-step calculation.
Common mistake
Rounding partway through and then carrying the rounded value forward is the most common way to lose the last mark on a long calculation. Keep the full value in the calculator and round once, at the answer.
Before you practise
- Learn each quantity with its unit as a pair, in both directions.
- To go from a large unit to a small one, multiply; from small to large, divide.
- kilo 10³, mega 10⁶, giga 10⁹; centi 10⁻², milli 10⁻³, micro 10⁻⁶, nano 10⁻⁹.
- An hour is 3600 s, and km/h to m/s is a division by 3.6.
- Standard form is a number between 1 and 10 times a power of ten.
- Give the answer to the same number of significant figures as the least precise value you were given, and round only at the end.