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VCE VCE VM Numeracy (Year 11) · Unit 1 — Number, Shape, Quantity and Measures, Relationships · 11m read

Quantity and Measures — Units, Time and Doses

Measurement is everywhere: shift times, recipes, medicine labels, fuel. Getting units right avoids costly — and sometimes dangerous — mistakes.

Learning objective: Convert between metric units, calculate time durations and interpret dosage and recipe quantities.

By the end of this lesson you can:

  • I can convert metric units of length, mass and capacity.
  • I can calculate durations using 24-hour time.
  • I can scale quantities and read dosage information.

Units are the language of measurement. Mixing up mL and L is like mixing up words in a sentence — the meaning changes completely.

Units and time

METRIC CONVERSIONS
• Length: 10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km.
• Mass: 1000 g = 1 kg; 1000 kg = 1 t.
• Capacity: 1000 mL = 1 L.
Multiply when converting to a smaller unit; divide when converting to a larger unit.

24-HOUR TIME — 1:30 pm = 13:30; 11:45 pm = 23:45.
DURATION — count hours, then minutes; subtract unpaid breaks.

SCALING RECIPES — multiply each ingredient by the scale factor (new serves ÷ original serves).

DOSES — follow the label or a pharmacist; check units (mg vs mL) and maximum doses.

Worked example (Medium)

A shift runs from 07:45 to 16:15 with a 30-minute unpaid break. How many paid hours?

  1. To the hour. 07:45 → 08:00 = 15 min.
  2. Whole hours. 08:00 → 16:00 = 8 h.
  3. Remaining. 16:00 → 16:15 = 15 min. Total = 8 h 30 min.
  4. Break. 8 h 30 min − 30 min = 8 h.

Answer: 8 paid hours.

Common mistakes

  • Treating time as decimal 1 h 30 min is 1.5 h, not 1.3 h. Fix: Divide minutes by 60 to get decimal hours.
  • Confusing mg and mL on medicine labels mg is mass of medicine; mL is volume of liquid. Fix: Use the label’s strength (e.g. mg per 5 mL) to convert.

Practice questions

  1. 2.5 L is equal to:

    1. 25 mL
    2. 250 mL
    3. 2500 mL
    4. 25 000 mL

    (1 marks)

  2. 45 minutes as a decimal of an hour is:

    1. 0.45 h
    2. 0.75 h
    3. 0.5 h
    4. 4.5 h

    (1 marks)

  3. A recipe for 4 people uses 300 g of rice. How much rice is needed for 10 people?

    (2 marks)

Summary

  • Smaller unit: multiply; larger unit: divide.
  • Use 24-hour time and subtract unpaid breaks.
  • Scale factor = new ÷ original.
  • Check mg vs mL on labels.

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