Units
Units
Your child may come across different units of measurement in their exam. There could be stand alone questions asking your child to convert between different units. The measurements your child is expected to be familiar with are length, mass and volume.
Length
Length is a measure of how long an object is. You can measure length with a ruler or a tape measure and units for length include metres, centimetres and miles.
Common conversions can be found below:
- 10 millimetres =1 centimetre
- 100 centimetres = 1 metre
- 1000 metres =1 kilometre
- 5 miles =8 kilometres
An important skill for your child to develop is converting between different units.
Given the facts stated above here are some examples that will help your child to get more comfortable with converting between different units of length.
Example: Convert 350 centimetres into metres.
We know that there are 100 centimetres in a metre. So, to find the number of metres that is equivalent to 350 centimetres we need to divide by \bold{\textcolor{darkturquoise}{100}}.
350 \div 100 = 3.5 metres
Example: Convert 10.2 kilometres into centimetres.
For this question we can use an in between conversion to metres before continuing to centimetres.
There are 1000 metres in a kilometre.
10.2 \times 1000 = 10\,200 metres
There are 100 centimetres in a metre.
10\,200 \times 100 = 1\, 020\, 000 centimetres
Example 1: Converting Between Miles and Kilometres
The conversions we have looked at so far have involved multiplying or dividing by 1000, but the method to convert between miles and kilometres has a different rule.
Example: Convert 24 kilometres into miles.
Using the rule above, your child should:
- Find the length in kilometres, which is 24 kilometres
- Divide the length in kilometres by 8.
24 \div 8 = 3
- Multiply the new value by 5
3 \times 5 = 15 miles
So, the final answer 24 kilometres is equal to 15 miles.
Mass
Mass is a measure of how heavy an object is. Mass can be measured using a weighing scale like something you would find in the kitchen.
The only units of mass that your child needs to be familiar with is grams and kilograms. The conversion rate is:
- 1000 grams = 1 kilogram
In their exam your child may be asked to convert between grams and kilograms.
Example: Convert 54\,500 grams into kilograms.
As we have seen above, there are 1000 grams in a kilogram. So, in order to find how many kilograms 54\,500 grams is we need to divide by \bold{\textcolor{darkturquoise}{1000}}.
54\,500 \div 1000 = 54.5 kilograms
Volume
The volume of a container is its capacity to hold something, usually a liquid like water. Volume can be measured using a measuring jug or a measuring cylinder.
Your child should make sure they are comfortable converting between litres and millilitres.
- 1000 millilitres =1 litre
Example: Convert 0.3 litres into millilitres.
There are 1000 millilitres in 1 litre, so we need to multiply by \bold{\textcolor{darkturquoise}{1000}}.
0.3 \times 1000 = 300 millilitres
Units Example Questions
Question 1: John has a bag of sugar that has a mass of 2.5 kilograms. 30 grams of sugar are spilt and John uses the rest in his cups of tea.
If John has 10 grams of sugar in each cup of tea, how many cups of tea can he make with the left over sugar?
[3 marks]
First, convert the masses into consistent units.
2.5 kilograms = 2.5 \textcolor{darkturquoise}{\times 1000} = 2500 grams.
Next, your child will need to subtract the mass of sugar that spilt.
2500 \textcolor{darkturquoise}{- 30} = 2470 grams
Now, we have the sugar that is left, which John uses for his cups of tea.
To find how many cups of tea he can make, divide the total mass of sugar by the mass of sugar per cup of tea.
2470 \textcolor{darkturquoise}{\div 10} = 247 cups of tea
Question 2: Farah is stood next to a block of flats. She is 150 centimetres tall. The building is 20 times taller than Farah.
What is the height, in metres, of the block of flats?
[2 marks]
Your child should be thinking about the fact we’ve been given a measurement in centimetres but need to give our final answer in metres.
Let’s convert 150 centimetres to metres.
150 \div 100 = 1.5 metres
To find the height of the block of flats multiply by 20 .
1.5 \times 20 = 30 metres
Question 3: Convert the following lengths.
a) 45 miles into kilometres
b) 64 kilometres into miles
[2 marks]
a) To convert miles to kilometres, your child will need to reverse the rule given above:
First divide the length in miles by \bold{\textcolor{darkturquoise}{5}}.
45 \textcolor{darkturquoise}{\div 5} = 9
Then, multiply the new value by \bold{\textcolor{blue}{8}}.
9 \textcolor{blue}{\times 8} = 72 kilometres
b) The length in kilometres is 64 kilometres
64 \div 8 = 8
Then, multiply by 5.
8 \times 5 = 40 miles