Grade 10 — Mathematics 10-3 › T3U01 SI Measurement

Grade 10 › T3U01 SI Measurement › L4
GRADE 10 · ALBERTAOUTCOME MAT10-3-M1

L4 · SI to imperial by proportional reasoning (factors provided)

Learning goal

“I can convert SI measurements to imperial units by setting up a proportion from a provided conversion factor, use the temperature formulas in both directions, and give a sensible approximation when an exact answer is not needed.”

Proportion — two equivalent fractions set equal: when 1 in = 2.54 cm, then (inches / 1) = (centimetres / 2.54).
Conversion factor — the provided fact that links two units: 1 inch = 2.54 cm. Factors are GIVEN in this course, never memorized.
Unit rate — the "per one" value: 2.54 cm per inch. Scaling the unit rate by the amount you have is the whole conversion.
Approximation — a close-enough value, marked with ≈, used when an exact conversion is unnecessary (1 inch ≈ 2.5 cm).
Worked example

A Canadian plan gives a shelf depth of 45 cm; a US pattern book works in inches. Provided factor: 1 inch = 2.54 cm. Build the proportion from the unit rate: every 1 inch matches 2.54 cm, so inches = centimetres / 2.54. 45 / 2.54 = 17.716... -> ≈ 17.7 in. Read the direction off the factor: centimetres are the smaller unit, so the inch count must be SMALLER than 45 - division is the right move, and 17.7 passes the reasonableness check. Second example, longer distance: a trail of 120 km in miles, factor 1 mile ≈ 1.6093 km: miles = 120 / 1.6093 = 74.566... -> ≈ 74.6 mi. Same shape every time: amount / (factor per unit).

Check yourself — explain it

To convert centimetres to inches we DIVIDE by 2.54 because...

Paired problem — example still visible

Convert 30 cm to inches (1 in = 2.54 cm) -> 30 / 2.54 = 11.81... -> ≈ 11.8 in

Faded completion — last step is yours

"Convert 200 cm to inches: inches = 200 / ___ = ___ in (nearest tenth)." -> 2.54; 78.7

Ready to practise?

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

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