Grade 10 — Mathematics 10-3 › T3U01 SI Measurement

GRADE 10 · ALBERTAOUTCOME MAT10-3-M1

L1 · The SI system: built on base ten; the six prefixes (milli to kilo)

Learning goal

“I can explain why the SI system was built on base ten, name the six prefixes from milli to kilo with their values, and match each prefix to its power of ten.”

SI system — the Systeme International: the metric measurement system used in Canada and almost every country, built entirely on base ten.
Base unit — the standard unit a family is built on: the metre for length, the gram for mass, the litre for capacity.
Prefix — a word-part added in front of a base unit to scale it: kilo-, hecto-, deca-, deci-, centi-, milli-.
Power of ten — how many tens are multiplied together: 100 is two tens (10 x 10); 1000 is three tens (10 x 10 x 10).
Worked example

Before SI, every region had its own units, and converting between them meant memorizing a new number for every pair. In the 1790s, French scientists built one system on the number our counting system already uses: ten. They defined the metre, then made every other length by scaling it by tens: 1 kilometre = 1000 metres, 1 metre = 100 centimetres, 1 centimetre = 10 millimetres. The same ladder works for grams and litres, unchanged. Say it plainly: in SI there is only ever one question - 'how many tens?' - and the prefix answers it.

Check yourself — explain it

SI conversions are simpler than imperial conversions because...

Paired problem — example still visible

A pharmacist measures a dose in milligrams, a truck's load in kilograms, and a patient's height in centimetres. What one fact about SI makes all three measurements easy to compare? -> All three are powers of ten of a base unit, so the same x10 ladder converts any of them.

Faded completion — last step is yours

"The gram family on the ladder: 1 kilogram = ___ grams, and 1 gram = ___ milligrams." -> 1000; 1000

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.