Lessons · Teaching · measurement, and converting a unit without guessing
Converting a unit is multiplying by one
Because 100 cm equals 1 m, the fraction 100 cm over 1 m equals one, and multiplying by it changes the unit without changing the quantity. Metric conversions move the decimal point because the steps are powers of ten; customary ones do not, so they need the factor written out.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
Every pupil asked to convert 250 cm to metres has a fifty-fifty chance of multiplying when they should divide, and the guess is invisible in the answer. Writing the conversion as a fraction makes the direction fall out of which unit cancels, so there is nothing to guess.
How to think about it
Write the quantity as a fraction over one. Multiply by a conversion fraction arranged so the unit you are leaving is on the opposite level and cancels. Whatever is left is the unit you wanted, and the arithmetic is then just arithmetic.
Worked example
250 cm to metres: multiply by 1 m over 100 cm, and cm cancelsArranging the fraction is the whole decision. The rest is division.
250 / 100 = 2.5 mFewer metres than centimetres, because a metre is the bigger unit.
3 feet to inches: multiply by 12 inches over 1 foot, giving 36 inchesGoing to a smaller unit gives a bigger number, always.
Metric prefixes: kilo is a thousand, centi is a hundredth, milli is a thousandthWhich is why metric conversions are a decimal point moving.
Your turn
Name what happens to the number when you convert to a smaller unit.
Converting to a smaller unit makes the number
Solve one, graded on the server
The trap
Converting an area or a volume with the length factor. A square metre is 10,000 square centimetres, not 100, because the factor is squared. A cubic metre is a million cubic centimetres.