GCSE physics, ages 14 to 16, about 15 minutes
Converting Units
Use prefixes and conversion factors to change the unit without changing the quantity.
97.5 MHz = 97 500 000 Hz
In standard form: 9.75 × 10⁷ Hz
Hz is a smaller unit than MHz, so the number gets bigger: multiply by 10⁶ (move the decimal point 6 places to the right).
72 km/h = 72 000 m ÷ 3600 s = 20 m/s
Ten questions, each in steps. A question counts only if every step is right first time. New numbers every time.
Why this mission needs it: Physics equations only work when every quantity is in compatible SI units: a mix-up between pound-seconds and newton-seconds famously lost the Mars Climate Orbiter.
The idea
- Value in the base unit, for example m, A, Hz
- The same quantity in the SI unit, ready to use in a formula.
- Value with a prefix, for example km, mA, MHz
- The number as you were given it, in a unit that carries a prefix.
- Prefix factor, power of ten
- What the prefix stands for: kilo is 10³, milli is 10⁻³, mega is 10⁶ and so on.
Same quantity, different number
A length of 2 km and a length of 2000 m are exactly the same distance. Converting units never changes the quantity; it changes the number and the unit together. A smaller unit needs a bigger number to describe the same thing.
Key point: Smaller unit, bigger number. Bigger unit, smaller number.
Prefixes are powers of ten
A prefix is shorthand for a power of ten: giga (G) is , mega (M) is , kilo (k) is , centi (c) is , milli (m) is , micro (μ) is and nano (n) is . To get to the base unit, replace the prefix with its power of ten: .
Key point: To reach the base unit, multiply by the prefix factor. To go back, divide by it.
Units made of two units
Units such as km/h are built from two units, so convert each one separately. For : the distance is and the time is , so the speed is .
Key point: To change km/h into m/s, divide by 3.6. To change m/s into km/h, multiply by 3.6.
Areas and volumes
Because , a square metre is and a cubic metre is . A common mistake is to use 100 for areas and volumes as well as lengths.
Key point: For an area, square the length factor. For a volume, cube it.
Where you’ll see this: In 1999 NASA lost the Mars Climate Orbiter because of a unit mix-up. One team's software reported thruster impulse in pound-force seconds, and the navigation software expected newton seconds. Nobody converted, the spacecraft approached Mars far too low, and it was lost.
Worked example
A radio station broadcasts at MHz. Write this frequency in hertz, in standard form.
- 1Read the prefix: mega (M) means .
- 2Replace the prefix with its power of ten: .
- 3Standard form needs a number between 1 and 10 at the front. Write as .
- 4Combine the powers of ten: .
Answer
Practice
Practise with the step-by-step quiz in the Try it panel. Each question is answered one step at a time, with fresh numbers every time, and the questions you miss come back for review.
Notes
Converting units
A physics formula only gives the right answer if every quantity is in units that fit together, normally the SI units: metres, kilograms, seconds, amperes and so on. Convert first, then put the numbers into the formula.
Prefixes
A prefix in front of a unit stands for a power of ten:
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| tera | T | 1 TW = 1 000 000 000 000 W | |
| giga | G | 1 GW = 1 000 000 000 W | |
| mega | M | 1 MHz = 1 000 000 Hz | |
| kilo | k | 1 km = 1000 m | |
| centi | c | 1 cm = 0.01 m | |
| milli | m | 1 mA = 0.001 A | |
| micro | μ | 1 μm = 0.000 001 m | |
| nano | n | 1 nm = 0.000 000 001 m |
To reach the base unit, replace the prefix with its factor. Take care with capitals: m is milli but M is mega.
Units made of two units
For a unit such as km/h, convert each part separately, as in the 72 km/h example in the idea above.
The shortcut: divide km/h by 3.6 to get m/s, and multiply m/s by 3.6 to get km/h.
Areas and volumes
Because :
Square the length factor for an area and cube it for a volume. Volumes of liquid are often in litres: , and litres.
Standard form
Very large and very small answers are written in standard form. The Moon is on average about 384 000 km from Earth:
A spacecraft lost to units
Writing the unit with every number, every time, is how engineers avoid mistakes like the one that lost the Mars Climate Orbiter.
Next on the journey
Once the units fit together, how do small motors move heavy parts on a rover or a launcher? That is the next lesson, on gears and turning forces.
Sources
The topics in these notes follow the Department for Education documents below.
- National curriculum in England: mathematics programmes of study (Department for Education)
- GCSE subject content for biology, chemistry and physics (Department for Education)
Where this fits in the curriculum
GCSE (key stage 4), building on key stage 3 in the curriculum for England.
The Department for Education says pupils should be taught to:
Key stage 3
“change freely between related standard units [for example time, length, area, volume/capacity, mass]”
GCSE: Working scientifically
“use prefixes and powers of ten for orders of magnitude (e.g. tera, giga, mega, kilo, centi, milli, micro and nano)”
GCSE: Working scientifically
“interconvert units”
Quoted from National curriculum in England: mathematics programmes of study and GCSE subject content for biology, chemistry and physics (Department for Education, gov.uk), checked on 12 October 2026. This is the content every exam board has to cover. It is not one board’s specification, so use your own for exactly what is examined.
Tick it off once the practice questions make sense.
Next on this mission
Free to use, not free to run: if this lesson helped you, your child or your class, chip in towards hosting and new lessons, or help review a mission.
Chip in on Ko-fiThis lesson was written with AI assistance. Check formulas and figures against your textbook or exam board’s specification before relying on them in assessed work.