Length Conversions

Lesson 4: Conversions Between SI and Imperial - Length Conversions

   Constructing Knowledge

Both imperial and SI length units are commonly used in Canada, so it is important to be able to convert between the two. You can use a conversion ratio and the proportional reasoning strategy used in previous lessons to convert between the length units in the SI and imperial systems.

   Multimedia

A video demonstrating length conversions between the SI and Imperial system is provided.

EXAMPLE 1

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Convert 20 kilometres to miles.

Solution

A conversion ratio for kilometres and miles is 1 km = 0.621 mi, which can be written as \(\frac{1\,\text{km}}{0.621\,\text{mi}}=1\) or \(\frac{0.621\,\text{mi}}{1\,\text{km}}=1\).

A proportion can be set up as follows:

\(\begin{align} \frac{y}{20\,\text{km}}&=\frac{0.621\,\text{mi}}{1\,\text{km}} \\ \\ \frac{y}{\cancel{20\,\text{km}}}\times {\color{red}{\cancel{20\,\text{km}}}}&=\frac{0.621\,\text{mi}}{1\cancel{\text{km}}}\times \color{red}{20\cancel{\text{km}}} \\ \\ y&=12.4\,\text{mi} \\ \end{align}\)

There are 12.4 miles in 20 kilometres.

EXAMPLE 2

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The longest par 5 in the US Open golf tournament history is 670 yards long. How long is the hole in metres?

Solution

A conversion ratio between yards and metres is 1 yd = 0.914 m , which can be written as \(\frac{1\,\text{yd}}{0.914\,\text{m}}=1\) or \(\frac{0.914\,\text{m}}{1\,\text{yd}}=1\)

A proportion can be set up as follows:

\(\begin{align} \frac{x}{670\,\text{yd}}&=\frac{0.914\,\text{m}}{1\,\text{yd}} \\ \\ \frac{x}{\cancel{670\,\text{yd}}}\times {\color{red}{\cancel{670\,\text{yd}}}}&=\frac{0.914\,\text{m}}{1\cancel{\text{yd}}}\times \color{red}{670\cancel{\text{yd}}} \\ \\ x&=612.4\,\text{m} \\ \end{align}\)

The golf hole is 612.4 metres long.




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