4.01 Units of length

Units of length

From smallest to largest these are common units used for measuring the length of something:

• millimetres (mm)
• centimetres (cm)
• metres (m)
• kilometres (km)

To determine the correct unit to use, and be able to estimate lengths it's useful to identify common objects that are about the length of the units above.

For example:

• $1$1 mm is about the thickness of a fingernail
• $1$1 cm is about the thickness of a finger
• $1$1 m is about the distance from the floor to the waist of an averagely tall person.
• $1$1 km is pretty hard to visualise, but imagine taking $1000$1000 steps - a kilometre is likely to be a bit more than that!

 

Practice questions

Question 1

Question 2

 

Choosing appropriate units

We can use any unit of measurement to measure something, but it makes sense to use a unit of measurement that:

• helps describe how long something is in a meaningful way, and
• makes it easier to measure.

An insect that is $8$8 mm long is easy to imagine, but if someone described the insect as being $0.000008$0.000008 km long, it would be tricky to imagine just how long it was.

 

Practice questions

Question 3

Question 4

 

Converting units of length

Converting from one unit to the other requires you to know how many of one unit makes up another. For example, $10$10 mm make up $1$1 cm. So, to convert from millimetres to centimetres we can divide by $10$10.

 

This conversion chart shows how to convert between neighbouring units.

We can also convert between any unit, even if it isn't neighbouring, just by going in smaller steps.

For example, to convert $1$1 km to centimetres:

$1$1 km$=$=$1\times1000$1×1000 m$=$=$1000$1000 m

We then convert from metres to centimetres:

$1000$1000 m$=$=$1000\times100$1000×100 cm$=$=$100000$100000 cm

So we can see that $1$1 km$=$=$100000$100000 cm.

 

Practice questions

Question 5

Question 6

Question 7

 

Imperial units of length

It may come as a surprise that the metric units of millimetres, centimetres, metres and kilometres are not universally used around the world, even though the metre is a part of the International System of Units (SI).

Imperial units are some of the most common units that are used in places where the metric units are not used.

For length, common imperial units are:

• an inch, denoted by the unit "in" or sometimes a double prime. For example, $3$3 inches$=$=$3$3 in$=$=$3"$3".
• a foot, denoted by the unit "ft" or sometimes a single prime. For example, $5$5 feet $4$4 inches$=$=$5$5 ft $4$4 in$=$=$5'4"$5′4".
• a mile, denoted by the unit "mi".

 

A foot is close to $30$30 cm (it is actually $30.48$30.48 cm). So in most cases, using $30$30 cm to approximate a foot gives a reasonable estimate of the size of the object in metric units.

An inch is $\frac{1}{12}$112​ of a foot. So it is about $2.5$2.5 cm ($2.54$2.54 cm to be exact). Again, using $2.5$2.5 cm is usually a close enough approximation to use as a gauge of the size. If an exact conversion is needed, such as if we are using the measurement in further calculations, then we can use the more exact conversion rate. But if someone says "move your foot $2$2 inches to the left", then knowing that's about $5$5 cm is probably enough.

A mile is just over $1.6$1.6 km. Equivalently, we can approximate that every $5$5 miles is $8$8 km.

 

Practice questions

Question 8

Question 9