Grade 10 — Mathematics 10C › C10U01 Measurement Systems & Conversions

Grade 10 › C10U01 Measurement Systems & Conversions › L3
GRADE 10 · ALBERTAOUTCOME AB-MAT10C-M1

L3 · Converting Within and Between Systems (Factors Provided)

Learning goal

“I can convert a measurement within or between the SI and imperial systems using proportional reasoning, verify the conversion with unit analysis, and check the answer for reasonableness with mental mathematics - using only the factors given.”

Conversion factor — a rate that equals 1, written as a fraction, e.g. 2.54 cm / 1 in. Multiplying by it changes the unit without changing the length.
Proportional reasoning — solving by keeping a ratio equal: if 1 in = 2.54 cm, then 5 in = 5 x 2.54 cm.
Unit analysis — tracking the units through a calculation so they cancel like variables: in x (cm/in) = cm. If the units don't land where you want, the setup is wrong.
Worked example

Convert 5 in to centimetres. Factor given: 1 in = 2.54 cm. Set up the proportion: the number of centimetres must be 2.54 times the number of inches. 5 x 2.54 = 12.7 cm. Unit analysis: 5 in x (2.54 cm / 1 in) - the inches cancel, centimetres remain. Sanity check: centimetres are smaller than inches, so the count should GROW: 12.7 > 5.

Check yourself — explain it

Why does the answer have MORE centimetres than the measurement had inches?

Paired problem — example still visible

9 in -> cm -> 22.86 cm (9 x 2.54)

Faded completion — last step is yours

"25 cm -> mm: 25 x 10 = ___ mm" -> 250 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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