GCSE · Physics · Edexcel · Spec 1PH0

Multiples and sub-multiples of units

5 m, 5 km, 5 mm: same number, same unit, yet the biggest is a million times the smallest. The whole difference is one letter.

Where does each prefix live?

The ladder of powers of ten

Each mark on this line is a power of ten: 3 means × 10³, −6 means × 10⁻⁶, and 0 is the plain unit with no prefix (metres, amps, joules…). Drag each prefix to the power of ten it stands for, then check your line.

Prefixed unit ⇄ base unit

Same current, two names
0 mA200 mA400 mA600 mA800 mA1000 mADrag: both readings move together

the current: 5/20. In milliamps 250 mA. In amps (base unit) 0.25 A

In milliamps250 mAIn amps (base unit)0.25 A

Drag the bar. The milliamp reading and the amp reading always describe exactly the same current.

Watch out: Multiplying by 10⁻³ makes a number smaller. If changing milliamps into amps made your number bigger, you went the wrong way.

Prefix to prefix

Count the steps, then choose the direction

Convert 6.5 km into centimetres. Give the answer in standard form and as an ordinary number.

  1. Find each prefix's power of ten: kilo = 10³, centi = 10⁻².
  2. missing step
Which line is step 2?

Convert first, then substitute

A heater transfers 1.8 MJ of energy in 600 s. What is its power? Before anything goes into the equation, the energy goes into joules: 1.8 MJ = 1.8 × 10⁶ J = 1 800 000 J. That's the number already waiting in the energy box.

Finding power (W)

P = E ÷ t

Answer

P = 1800000 ÷ 600

= 3000 W

The kilogram exception

Spot the line that loses the mark

A 1.2 kg ball moves at 5 m/s. Calculate its kinetic energy using Eₖ = ½ × m × v².

A student's answer — which line goes wrong?

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

k, M, m, μ: each prefix is just a power of ten stuck onto a unit. Put them all on one scale and every conversion becomes counting steps.

What you need to know

  • The power of ten that each prefix from giga to nano stands for.
  • How to convert a prefixed quantity to the base unit, and back again.
  • How to convert between two prefixes using the difference in their powers.
  • How prefixes link to standard form.
  • Why quantities must be in base SI units before they go into an equation, and why the kilogram is the base unit of mass.

The big picture

A prefix multiplies a unit by a power of ten: giga (G) 10⁹, mega (M) 10⁶, kilo (k) 10³, centi (c) 10⁻², milli (m) 10⁻³, micro (μ) 10⁻⁶, nano (n) 10⁻⁹. To reach the base unit, multiply by the prefix's power; to go the other way, divide by it. Between two prefixes, use the difference in their powers. In standard form the prefix replaces the power of ten, so 5 × 10⁻⁹ m = 5 nm. Convert everything to base SI units before substituting into an equation, and remember the base unit of mass is the kilogram.

Key points

1A prefix multiplies a unit by a power of ten, so 3 kW means 3 × 10³ W.
2G = 10⁹, M = 10⁶, k = 10³, c = 10⁻², m = 10⁻³, μ = 10⁻⁶, n = 10⁻⁹. Capital M (mega) and small m (milli) are very different.
3To reach the base unit, multiply by the prefix's power of ten: 250 mA = 250 × 10⁻³ A = 0.25 A. To go from the base unit to a prefixed unit, divide by it.
4Between two prefixes, the conversion is the difference in their powers: kilo (3) to milli (−3) is 6, so 1 km = 10⁶ mm.
5A prefix can stand in for the power of ten in standard form: 5 × 10⁻⁹ m = 5 nm.
6Convert every quantity to base SI units before substituting. The base unit of mass is the kilogram, so divide grams by 1000.

Worked example

Problem

A metal block has a mass of 540 g and a volume of 2.0 × 10⁻⁴ m³. Calculate its density in kg/m³, using density = mass ÷ volume.

⚠ Watch out

Changing kilograms into grams 'to get to the base unit'. The kilogram IS the base unit of mass, so a mass in kilograms goes straight into the equation, while a mass in grams is divided by 1000 first.

🧠

Memory hook

Every prefix is a step on one ladder of powers of ten. Count the steps between two prefixes, then ask: am I moving to a smaller unit? Then I need more of them, so the number gets bigger. And remember, the kilogram is already home.

✓

Check yourself

Without a calculator: how many milliwatts are in 2 kW? (Kilo and milli are six steps apart, and milliwatts are smaller, so 2 kW = 2 × 10⁶ mW.)

Flashcards

(11)
What does putting a prefix in front of a unit do?
It multiplies the unit by a power of ten, so very large and very small quantities can be written compactly.
The large prefixes: what are G, M and k?
Giga = 10⁹, mega = 10⁶, kilo = 10³.
The small prefixes: what are m, μ and n?
Milli = 10⁻³, micro = 10⁻⁶, nano = 10⁻⁹.
Which prefix breaks the pattern of multiples of 3, and what is it?
Centi (c) = 10⁻², a hundredth.
M or m: what is the difference?
Capital M is mega (10⁶); small m is milli (10⁻³). They are 10⁹ apart.
Into the base unit, or out of it: multiply or divide?
Into the base unit: multiply by the prefix's power (7 μs = 7 × 10⁻⁶ s). Out of it: divide (45 000 W ÷ 10³ = 45 kW).
How do you convert between two prefixes?
Use the difference in their powers of ten, e.g. milli (−3) to micro (−6) is 3, so 1 mm = 10³ μm.
How do prefixes link to standard form?
The prefix replaces the power of ten: 3 × 10⁻⁶ A = 3 μA.
What must you do to every quantity before substituting it into a physics equation?
Convert it to base SI units, such as metres, kilograms, seconds and amperes.
What is the base SI unit of mass?
The kilogram, even though it has a prefix. Divide a mass in grams by 1000 to get kilograms.
Converting to a smaller unit: does the number get bigger or smaller?
Bigger. You need more of the smaller unit to make the same quantity.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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