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Numbers, units and arithmetic
Numbers, units and arithmetic

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2.6 Comparing measurements

In order to compare quantities, it is best to express them in the same units.

Example 10

Three children have just measured their own heights in metric units. Isaac says ‘My height is 1098’, Jasmine says ‘My height is 112’ and Kim says ‘Mine is 1.1’. What units were they using? Who is the tallest?

Answer

First decide what units the children were using and then convert all the measurements to the same units. It is reasonable to guess that the heights are between 1 and 2 metres. (A height between 10 cm and 20 cm would mean they were not yet born, whereas a height between 10 m and 20 m would make them as tall as a house!) So Isaac has given his height in millimetres and his height in metres is 1098 ÷ 1000 = 1.098 m. Jasmine has given her height in centimetres, so her height in metres is 112 ÷ 100 = 1.12 m. Kim's height is in metres already, so Kim is 1.1 m tall. So, the heights in metres are:

Isaac1.098
Jasmine1.120
Kim1.100

(Inserting a 0 to the right of Jasmine's 1.12, and two 0s to the right of Kim's 1.1, has no effect on the value but is useful for comparisons as here.)

Comparing from the left, all have 1s in the units column. Isaac has a 0 in the tenths column, but Jasmine and Kim have 1s in the tenths column. So Jasmine and Kim are both taller than Isaac. In the hundredths column, Jasmine has 2 and Kim has 0. So Jasmine is the tallest.