Converting measurements

Do you know your height in centimetres and your weight in stones and pounds? Do you cycle for 5 miles but run 100 metres? Despite efforts to 'turn metric', it is obvious that there are still many imperial units in use today. It is therefore helpful to know how to convert between the two.

1. Converting from one metric unit to another
2. Converting between metric and imperial units

Converting from one metric unit to another

Perhaps the most common metric conversion is that between mm, cm, m and km.

1cm = 10mm

1m = 100cm = 1000mm

1km = 1000m = 100 000cm = 1 000 000mm

kilo means 1000, so 1km = 1000m

centi means ¹/₁₀₀, so 1cm = ¹/₁₀₀^th m

milli means ¹/₁₀₀₀, so 1mm = ¹/₁₀₀^th m

Once you are confident with conversions between mm, cm, m and km, converting units of mass and capacity is easy!

Examples:

1km = 1000m, so 1kg = 1000g

1m = 100cm, so 1l (litre) = 100cl (centilitres)

1m = 1000mm, so 1g = 1000mg (milligrams)

Question 1

A packet of biscuits weighs 150g. Find the weight of 12 packets of biscuits:

1. in g
2. in kg

The Answer

1. Did you get the answer 1800g?
   Well done! 12 × 150 = 1800, so 12 packets of biscuits weigh 1800g.
2. Did you get the answer 1.8kg?
   Well done! If not, remember that 1kg = 1000g. To convert from g to kg, we divide by 1000.

Converting between metric and imperial units

Here are some examples of metric and imperial measures of length, mass and capacity:

	Metric	Imperial
Length	mm, cm, m, km	inch, foot, yard, mile
Mass	mg, g, kg	ounce (oz), pound (lb), stone
Capacity	ml, cl, l	pint, gallon

You will be expected to know some common conversions between metric and imperial units. Some of these are shown below, but check with your teacher which ones you need to learn.

1km = mile
1m = 39.37 inches
1 foot = 30.5cm
1 inch = 2.54cm
1kg = 2.2lb
1 gallon = 4.5 litres
1 litre = 1 ³/₄ pints

Question 1

A cup has a circumference of 10 inches. What is it in cm?

The Answer

We know that 1 inch = 2.54cm.
We are converting from inches to cm, so we multiply by 2.54.
10 × 2.54 = 25.4cm.

It is easy to get confused over whether to multiply or divide, so here is a way to check your answers:

After doing the conversion, always think about whether your answer should be bigger or smaller than the original number.

In this question, which involves converting inches into cms, we know that cms are smaller than inches, so you should end up with a bigger number than the one you started with. You therefore need to multiply.

Question 2

Use this method to say which of the following conversions are definitely incorrect?

61cm = 1860.5 feet
5 gallons = 22.5 litres
14lb = 30.8kg

The Answer

Did you get the answer 61cm = 1860.5 feet and 14lb = 30.8kg? If so - well done!

1). Which units would you use to describe the length of a hockey pitch? a) mm b) cm c) m d) km 2). Which units would you use to describe the distance from Glasgow to London? a) mm b) cm c) m d) km In questions 3-8, convert the quantities to the given units. 3). 58km = m 4). 2400mg = g 5). 168cl = l 6). 25 gallons = l 7). 122cm = feet 8). 40km = miles The width of one hardback book is 17mm. How many books will fit on a shelf that's 34cm long? 9). books 10). Which shop offers the best price? a) Allen's b) Baker's

1. Which units would you use to describe the length of a hockey pitch?
Metres are the most appropriate units to describe the length of a hockey pitch.

2. Which units would you use to describe the distance from Glasgow to London?
Kilometres are the most appropriate units to describe the distance from Glasgow to London.

3. In questions 3-8, convert the quantities to the given units.

58km = m
Did you remember to multiply by 1000?

4. 2400mg = g
did you remember to divide by 1000?

5. 168cl = l
Did you remember that 1l (litre) = 100cl (centilitres)?

6. 25 gallons = l
Did you remember to multiply by 4.5?

7. 122cm = feet
Did you remember to divide by 30.5?

8. 40km = miles
Try to revise the rules for multiplying fractions.

9. The width of one hardback book is 17mm. How many books will fit on a shelf that's 34cm long?



books
Remember that 34cm = 340mm.

10.
Which shop offers the best price?
2 litres = 3½ pints, so you get more milk for 89p in shop B.