Converting rates

Change units without changing the situation.

Change units without changing the situation.

Use equivalent measurements

1 h = 60 min = 3600 s and 1 km = 1000 m. Conversion factors represent 1, such as 1000 m / 1 km. Choose their direction so unwanted units cancel.

Make a prediction · test a relationship

See the quantities change.

Predict before changing a value. The written explanation below remains available without JavaScript.

Convert the numerator and denominator

72 km/h × 1000 m/km ÷ 3600 s/h = 20 m/s. Dividing by 3.6 converts km/h to m/s; multiplying by 3.6 converts m/s to km/h. Understand the units before memorising a shortcut.

More units can mean a bigger numerical value

For the same speed, metres per second and kilometres per hour have different numbers. Predict whether the conversion is sensible. Do not round partway through a chain of conversions.

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Pause the explanation before a calculation. Predict the next step and explain which quantities are being compared.

Follow the reasoning

Worked examples

Convert 54 km/h to m/s.

  1. 54 × 1000 = 54000 m per hour.
  2. 54000 ÷ 3600 = 15 m/s.
  3. Check: 15 × 3.6 = 54 km/h.

A pump moves 2.5 L/min. Convert to mL/s.

  1. 2.5 L/min = 2500 mL/min.
  2. 2500 ÷ 60 = 125/3 mL/s.
  3. Approximately 41.67 mL/s; keep 125/3 for later exact calculations.

Try it before checking.

Convert 10 m/s to km/h.

A first hint

Convert metres to kilometres, then seconds to hours.

Compare your reasoning

10 × 3600 ÷ 1000 = 36 km/h.

Practise the skill.

Fresh questions · useful feedback

Build fluency, one decision at a time.

Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.

0 of 8 questions completed

Enter a number, decimal or fraction such as −3/2. Include the sign; leave out units.

This round saves on this device. It is practice, not a school mark.

Explain a little more.

Explain why multiplying by 1000 and dividing by 3600 gives the same result as dividing by 3.6.

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Keep the connections going.

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