7.1 Units of measure and conversions — Learn

Prerequisites: decimal place value and multiplying or dividing by 10.

Before you begin

You should know decimal place value and how to multiply and divide by 10.

Objectives

• Convert between metric units for length, mass, capacity and area.
• Use scale drawings and map scales to find real distances and lengths.
• Read and use bearings measured clockwise from north.

Metric conversions

The prefixes kilo-, centi- and milli- mean $1000$, one hundredth and one thousandth. A conversion changes the number and its unit together.

For area, square the length conversion: $1\text{ m}^2=10\,000\text{ cm}^2$.

Example 1. Convert $3.6$ km to metres.

So $3.6$ km is $3600$ m. Convert back by dividing by $1000$.

Example 2. Convert $2.4\text{ m}^2$ to $\text{cm}^2$.

So the area is $24\,000\text{ cm}^2$.

Watch out. A common error is to multiply a square measure by $100$. Area has two length dimensions, so use $100^2$. For example, $1\text{ m}^2=10\,000\text{ cm}^2$.

Scale drawings

A scale gives the ratio between a drawing length and a real length in matching units. A scale of $1:50\,000$ means $1$ cm represents $50\,000$ cm, or $500$ m.

Example 3. A map uses scale $1:50\,000$. Two places are $4.2$ cm apart. Find their real distance in kilometres.

Bearings

A bearing is an angle measured clockwise from north. Write it with three digits, such as $065^\circ$. The north line is the starting direction.

Example 4. A bearing of $125^\circ$ turns $125^\circ$ clockwise from north. Its reverse bearing is $125^\circ+180^\circ=305^\circ$.

Progress check. A route is $3$ cm on a $1:25\,000$ map. Predict its real distance before converting.

Predict: If you double the drawing length, what happens to the real length? Test: Set the scale slider to $1$, then to $2$. Explain: Write how the scale ratio connects the two lengths.

You should now be able to

• convert metric lengths, masses, capacities and areas;
• use a scale ratio to find a real distance or drawing length;
• measure and write a three-figure bearing from north.