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MathidiaMathematics Academy
Proportion and rates of change
Lesson 39 of 75
Challenge

Speed conversions

Objective. Convert rates between compound units.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Converting speed between compound units, such as from metres per second to kilometres per hour, requires converting both the distance unit and the time unit consistently. To change m/s to km/h, multiply by 3600 (seconds in an hour) to scale up time, then divide by 1000 (metres in a kilometre) to scale down distance, which together is the same as multiplying by 3.6. For example, 20 m/s converts to 20 × 3.6 = 72 km/h. Converting the opposite way, from km/h to m/s, divides by 3.6 instead. Keeping track of which unit is on top and which is on the bottom prevents multiplying and dividing the wrong way.

Worked example

Convert a speed of 108 km/h into metres per second.

108
Illustrated card showing 108
  1. 1Converting from km/h to m/s requires dividing by 3.6.
  2. 2Substitute the value: 108 ÷ 3.6.
  3. 3Carry out the division carefully: 108 ÷ 3.6 = 30.
  4. 4Attach the correct units: metres per second.

Answer: 30 m/s

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Common mistake. Pupils often multiply by 3.6 when converting from km/h to m/s instead of dividing, since they forget the conversion direction matters. Multiply by 3.6 going from m/s to km/h, and divide by 3.6 the other way.

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