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Math 10C

Math 10C · Worksheets

Measurement and conversion

Ten questions of mixed difficulty, covering Measurement. Print it, or work through it on screen — the answer key starts on its own page.

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Measurement and conversion

Math 10C · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. A car travels at 90 km/h. In metres per second that is

    1. a) 0.025 m/s
    2. b) 25 m/s
    3. c) 1500 m/s
    4. d) 54 m/s

  2. A length of 15 inches, with 1 inch = 2.54 cm, is about

    1. a) 38.1 cm
    2. b) 6.4 cm
    3. c) 5.9 cm
    4. d) 39.4 cm

  3. A recipe needs 2 cups of liquid and 1 cup is 250 mL. In litres that is

    1. a) 0.25 L
    2. b) 0.5 L
    3. c) 2.5 L
    4. d) 500 L

  4. There are 12 inches in a foot and 3 feet in a yard, so one yard is

    1. a) 30 inches
    2. b) 24 inches
    3. c) 15 inches
    4. d) 36 inches

  5. A room is 12 ft by 15 ft. Its area in square metres, with 1 ft = 0.3048 m, is about

    1. a) 54.9 m²
    2. b) 16.7 m²
    3. c) 180 m²
    4. d) 5.5 m²

  6. Of these, the imperial unit of mass is the

    1. a) pound
    2. b) kilogram
    3. c) gram
    4. d) tonne

  7. Of these measurements, the most precise is

    1. a) 5 cm
    2. b) 4.5 cm
    3. c) 4 cm
    4. d) 4.50 cm

  8. The SI base unit of length is the

    1. a) kilometre
    2. b) inch
    3. c) centimetre
    4. d) metre

  9. A conversion factor such as 100 cm / 1 m is useful because it is equal to

    1. a) one centimetre
    2. b) one
    3. c) one metre
    4. d) one hundred

  10. A map has a scale of 1 : 50 000. A distance of 6 cm on the map represents

    1. a) 30 km
    2. b) 3 km
    3. c) 500 m
    4. d) 300 m

Answer key · Measurement and conversion

Math 10C · maddyhelps.com

  1. b) 25 m/s — 90 km/h × 1000 m/km ÷ 3600 s/h = 25 m/s. Dividing km/h by 3.6 is the shortcut, and it comes from exactly that chain.
  2. a) 38.1 cm — 15 × 2.54 = 38.1 cm. A centimetre is smaller than an inch, so the number must get bigger. Dividing instead gives 5.9, which would be a length shorter than the original in bigger units — impossible.
  3. b) 0.5 L — 2 × 250 = 500 mL, and 1000 mL make a litre, so 0.5 L. Two conversions in a row: first to the unit you were given a factor for, then to the one asked for.
  4. d) 36 inches — Multiply along the chain: 3 × 12 = 36. Imperial conversions have to be memorised because the numbers are not consistent — 12, 3, 5280 — which is exactly why SI was invented.
  5. b) 16.7 m² — Convert first: 12 ft = 3.658 m and 15 ft = 4.572 m, so the area is 16.7 m². Converting the area directly needs the factor <i>squared</i> — 180 ft² × 0.3048² = 16.7 m² — and forgetting to square it is the classic error.
  6. a) pound — Pounds and ounces are imperial; grams, kilograms and tonnes are SI. Roughly, a kilogram is about 2.2 pounds, which is worth knowing as a sanity check.
  7. d) 4.50 cm — Precision is about the smallest unit the instrument could read. 4.50 cm claims hundredths of a centimetre; 4.5 cm only claims tenths. The trailing zero is doing real work and should not be dropped.
  8. d) metre — SI builds every other length from the metre using prefixes: a kilometre is a thousand metres, a centimetre is a hundredth. The inch belongs to the imperial system, which is not built on powers of ten at all.
  9. b) one — 100 cm and 1 m are the same length, so the fraction is 1. Multiplying by 1 changes the units without changing the quantity, which is why unit analysis works at all.
  10. b) 3 km — 6 cm × 50 000 = 300 000 cm. Then 300 000 ÷ 100 = 3000 m = 3 km. A scale is a ratio of the same units, so convert only after multiplying.