Each metric prefix stands for a fixed power of ten: kilo = 10³, centi = 10⁻², milli = 10⁻³, micro = 10⁻⁶, nano = 10⁻⁹. To convert between two prefixes, find the gap between their powers of ten and move the decimal point that many places: right when going from a bigger unit to a smaller unit, left when going the other way. Get the direction right and every conversion becomes a single decimal-point shift.
Prefix conversion looks trivial, which is exactly why it costs marks. Students memorise "kilo means 1000" without pinning down whether multiplying or dividing by 1000 is the correct move for the direction they are converting. Under exam pressure, the decimal point moves the wrong way, and an otherwise correct calculation ends up out by a factor of a thousand, a million, or worse.
The fix is to stop thinking in words like "kilo" and start thinking in powers of ten. Once every prefix is just a number written as 10ⁿ, the conversion is pure arithmetic: subtract the powers, move the decimal point.
Step 1
Write each prefix as 10ⁿ
Step 2
Find the gap between the two powers
Step 3
Bigger unit to smaller unit: number gets bigger
Step 4
Move the decimal point that many places
The eight prefixes that appear most often in O-Level E-Math and science, from largest to smallest, with the base unit sitting in the middle:
10³ = 100010² = 10010¹ = 1010⁰ = 110⁻¹ = 0.110⁻² = 0.0110⁻³ = 0.00110⁻⁶ = 0.00000110⁻⁹ = 0.000000001Convert 4.5 km to metres.
Solution
10³, and the base unit (metre) = 10⁰.3 − 0 = 3 places.4.5 km = 4.5 × 10³ m = 4500 mConvert 250 ml to litres.
Solution
10⁻³, and the base unit (litre) = 10⁰.0 − (−3) = 3 places.250 ml = 250 ÷ 10³ = 0.25 lConvert 0.6 μm to nanometres. This is the case that catches most students: neither prefix is the base unit.
Solution
10⁻⁶, nano = 10⁻⁹.−6 − (−9) = 3 places.0.6 μm = 0.6 × 10³ nm = 600 nmThe step students get wrong
Deciding which way the decimal point moves. The rule is fixed: going from a bigger unit to a smaller unit always makes the number bigger (you need more of the smaller unit to describe the same amount), so the decimal point moves right. Going from a smaller unit to a bigger unit always makes the number smaller, so the decimal point moves left. If your answer after converting looks smaller than the original but you went from a bigger unit to a smaller one, you moved it the wrong way. Check by asking: does this unit describe a bigger or smaller amount than the one I started with?
First, the size of the shift. For any two prefixes it is simply the difference between their powers of ten, and that holds even when neither prefix is the base unit, as in worked example 3 above. Second, check what the question is actually measuring.
Exam tip: if a question mixes area or volume with prefixes, for example converting cm² to m², the shift is not the same as for length. Since area involves two lengths multiplied together, the shift is 10² for every 10¹ in length, so 1 m² = 10⁴ cm², not 10². Volume uses 10³ per 10¹ in length. Check whether the question is asking about length, area, or volume before applying the shift.
How is this related to standard form?
Every metric prefix is really shorthand for a number written in standard form: kilo is × 10³, milli is × 10⁻³, and so on. If a conversion answer looks awkward as an ordinary number, for example 0.000000001, it is often clearer to write it in standard form instead. See standard form for the full conversion method.
Do I need to memorise all eight prefixes?
For O-Level E-Math, kilo, centi, milli, micro and nano are the ones that appear most often, alongside the base unit. Hecto, deca and deci rarely appear in exam questions, but they are worth a glance because they show that the pattern is continuous. Memorise the power of ten for each prefix rather than a vague sense of "big" or "small".
How many decimal places should my final answer have?
A prefix conversion itself does not change how many significant figures are meaningful in your answer, it only changes the unit. If the question also asks you to round, apply the rounding rule from significant figures vs decimal places after you have converted, not before.
What if the two prefixes are both smaller than the base unit, like centi to nano?
The method is identical. centi = 10⁻², nano = 10⁻⁹, so the gap is −2 − (−9) = 7 places. Centimetre is the bigger of the two units, so the number gets bigger and the decimal point moves 7 places right: 1 cm = 1 × 10⁷ nm = 10 000 000 nm.
— Mr Gan Math Tuition
Mr. Gan works with students who want the powers-of-ten method locked in before it costs marks in the exam hall.
Chat with Mr. Gan