Grade 10 — Mathematics 10-3 › T3U01 SI Measurement

Grade 10 › T3U01 SI Measurement › L3
GRADE 10 · ALBERTAOUTCOME MAT10-3-M1

L3 · Converting within SI; why SI uses decimals

Learning goal

“I can convert between SI units in both directions by counting ladder steps - multiply going down to smaller units, divide coming up to larger units - and explain why SI measurements are written as decimals instead of fractions.”

Convert — to rewrite the same measurement in a different unit. The amount does not change; only its name does.
Equivalent measurement — two measurements of exactly the same amount in different units: 1.5 m and 150 cm are equivalent.
Ladder step — one move between neighbouring units on the prefix ladder; each step is worth exactly x10 or /10.
Worked example

Convert 3.2 m to centimetres using BOTH representations. Ladder: metre -> centimetre is two steps down, and each step is x10, so the conversion is x100: 3.2 x 100 = 320 cm. Proportion table (same fact, second representation): 100 cm / 1 m = ? cm / 3.2 m - scale the unit rate by 3.2: 100 x 3.2 = 320 cm. Same answer, as it must be. Notice WHY the point slides: the unit got smaller, so it takes MORE of them to measure the same length. Smaller unit, bigger number - always.

Check yourself — explain it

Converting 0.45 km to metres gives a bigger number (450) because...

Paired problem — example still visible

Convert 0.45 km to metres -> 3 steps down (km -> m), x1000: 0.45 x 1000 = 450 m

Faded completion — last step is yours

"Convert 2.05 m to millimetres: two steps to cm, one more to mm, so x1000 altogether: 2.05 x 1000 = ___ mm." -> 2050 mm

Ready to practise?

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

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