What is the difference between metric and imperial units?

Metric units are the international standard units of measurement, such as metres, grams and litres. Imperial units, such as miles, pounds and gallons, were once common in the UK and are still used in some places, though most measurement is now metric.

True or False? A millilitre and a cubic centimetre are the same size.

True. One millilitre is exactly one cubic centimetre, so the two are interchangeable. That is why the capacity of a cup can be written either as 250 ml or as 250 cm cubed without changing anything.

How do you decide which metric unit of length to use?

Choose the unit that gives a sensible-sized number for the thing you are measuring. Millimetres suit the thickness of a coin, centimetres the span of a hand, metres the length of a bus, and kilometres the distance between towns.

What units other than length, mass and volume might you meet?

Three more sets come up regularly: temperature, in degrees Celsius or degrees Fahrenheit time, in seconds, minutes and hours money, in pounds, dollars or euros Each still needs a unit written with the answer, exactly as a length does.

True or False? Converting between metric units always means multiplying or dividing by a power of 10.

True. The metric system is built on base 10, so every conversion between metric units is a multiplication or division by 10, 100, 1000 and so on. Imperial conversions are not powers of 10, which is what makes them much less convenient to work with.

How do you find the conversion factor for cubic units?

Cube the ordinary conversion factor. Since 1 cm = 10 mm and 10 cubed is 1000, one cubic centimetre is 1000 cubic millimetres. The same reasoning gives 1 cubic metre as 1 000 000 cubic centimetres, because 100 cubed is a million.

How can you check that a conversion has gone the right way round?

Ask whether the answer ought to be a bigger or a smaller number than you started with. A centimetre is larger than a millimetre, so 2 centimetres must come to more than 2 millimetres, not less; an answer of 0.2 mm would be the wrong way round.

Define compound unit .

A compound unit is a measurement worked out from more than one other measurement. Kilometres per litre combines a distance and a volume, and grams per cubic centimetre combines a mass and a volume.

What does a rate tell you?

How much one quantity changes when the other goes up by one . So 50 kilometres per litre means the car covers 50 kilometres for each single litre of fuel it uses.

How can a rate such as 50 kilometres per litre be used as a conversion factor?

Rewrite it as the equivalence 1 litre = 50 kilometres. Multiply to turn litres into kilometres, so 3.5 litres covers 175 kilometres. Divide to turn kilometres into litres, so 110 kilometres needs 2.2 litres.

True or False? Fuel consumption measured in kilometres per litre gets better as the number gets larger.

True. More kilometres for each litre means the car travels further on the same fuel. Watch the direction of the unit though: fuel consumption given the other way round, as litres per kilometre, is better when the number is smaller .

Why must you check the units before dividing a distance by a time?

Because the units of the answer come straight from the units you put in. An answer in metres per second needs the distance in metres and the time in seconds, so a distance in kilometres or a time in minutes has to be converted first. This is the commonest place marks are lost in this topic.

True or False? 3.7 metres per second and 13.3 kilometres per hour describe the same speed.

True. They are the same speed written in different units, since 3.7 metres per second covers 13 320 metres in an hour. The number attached to a speed means nothing on its own: the units have to be read with it.

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Units & Quantities (SQA National 5 Applications of Mathematics): Flashcards

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What is the difference between metric and imperial units?

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What is the difference between metric and imperial units?
Metric units are the international standard units of measurement, such as metres, grams and litres.
Imperial units, such as miles, pounds and gallons, were once common in the UK and are still used in some places, though most measurement is now metric.
True or False?
A millilitre and a cubic centimetre are the same size.
True.
One millilitre is exactly one cubic centimetre, so the two are interchangeable.
That is why the capacity of a cup can be written either as 250 ml or as 250 cm cubed without changing anything.
Complete the units for mass and volume:
Mass is measured in grams and in $______$ for heavier objects, while volume is measured in millilitres and in $______$ for larger amounts.
The completed sentence is:
Mass is measured in grams and in kilograms for heavier objects, while volume is measured in millilitres and in litres for larger amounts.
So an apple is weighed in grams but a whale in kilograms, and a cup holds millilitres where a bath holds litres.
How do you decide which metric unit of length to use?
Choose the unit that gives a sensible-sized number for the thing you are measuring.
Millimetres suit the thickness of a coin, centimetres the span of a hand, metres the length of a bus, and kilometres the distance between towns.
What units other than length, mass and volume might you meet?
Three more sets come up regularly:
- temperature, in degrees Celsius or degrees Fahrenheit
- time, in seconds, minutes and hours
- money, in pounds, dollars or euros
Each still needs a unit written with the answer, exactly as a length does.
True or False?
Converting between metric units always means multiplying or dividing by a power of 10.
True.
The metric system is built on base 10, so every conversion between metric units is a multiplication or division by 10, 100, 1000 and so on.
Imperial conversions are not powers of 10, which is what makes them much less convenient to work with.
Complete the metric length conversions you have to know:
$1 cm =______mm, 1 m =______cm and 1 km =______m$
The completed conversions are:
$1 cm = 10 mm, 1 m = 100 cm and 1 km = 1000 m$
These are the metric conversions you are expected to know; any imperial ones will be given to you.
You are told that 1 gallon = 4.546 litres. How do you convert 20 litres into gallons?
Divide by the conversion factor, because you are going from the second unit back to the first.
That gives $20 \div 4.546 = 4.3995 . . .$ , so 20 litres is about 4.40 gallons.
Going the other way, from gallons into litres, you would multiply instead.
Complete the remaining conversions you have to know:
$1 kg =______g, 1 L =______ml and 1 hour =______minutes$
The completed conversions are:
$1 kg = 1000 g, 1 L = 1000 ml and 1 hour = 60 minutes$
Note that a minute is 60 seconds as well, so time is the one set here that does not run in powers of 10.
True or False?
$1 m^{2} = 100 {cm}^{2}$
False.
When the unit is squared, the conversion factor has to be squared too.
Since 1 m = 100 cm and 100 squared is 10 000, the correct statement is that 1 square metre is 10 000 square centimetres.
How do you find the conversion factor for cubic units?
Cube the ordinary conversion factor.
Since 1 cm = 10 mm and 10 cubed is 1000, one cubic centimetre is 1000 cubic millimetres.
The same reasoning gives 1 cubic metre as 1 000 000 cubic centimetres, because 100 cubed is a million.
Convert 0.4 miles into metres, given that 1 mile = 1.609 km.
0.4 miles is 643.6 metres.
This needs two conversions in turn: $0.4 \times 1.609 = 0.6436$ km.
Then convert kilometres into metres: $0.6436 \times 1000 = 643.6$ m.
How can you check that a conversion has gone the right way round?
Ask whether the answer ought to be a bigger or a smaller number than you started with.
A centimetre is larger than a millimetre, so 2 centimetres must come to more than 2 millimetres, not less; an answer of 0.2 mm would be the wrong way round.
Define compound unit.
A compound unit is a measurement worked out from more than one other measurement.
Kilometres per litre combines a distance and a volume, and grams per cubic centimetre combines a mass and a volume.
What does a rate tell you?
How much one quantity changes when the other goes up by one.
So 50 kilometres per litre means the car covers 50 kilometres for each single litre of fuel it uses.
Complete what each compound unit measures:
Speed measures how far you travel for each unit of $______$ that passes, while population density measures how many people there are for each unit of $______$ of land.
The completed sentence is:
Speed measures how far you travel for each unit of time that passes, while population density measures how many people there are for each unit of area of land.
Flow rate and fuel consumption work the same way, measuring volume per unit of time and fuel per unit of distance.
How can a rate such as 50 kilometres per litre be used as a conversion factor?
Rewrite it as the equivalence 1 litre = 50 kilometres.
Multiply to turn litres into kilometres, so 3.5 litres covers 175 kilometres.
Divide to turn kilometres into litres, so 110 kilometres needs 2.2 litres.
A car averages 64 kilometres per gallon and a journey is 251 kilometres. How many litres of fuel are needed, given 1 gallon = 4.546 litres?
About 17.8 litres are needed.
Using the rate as a conversion factor gives $251 \div 64 = 3.92 . . .$ gallons.
Converting that into litres gives $3.92 \times 4.546 = 17.8 . . .$ litres.
True or False?
Fuel consumption measured in kilometres per litre gets better as the number gets larger.
True.
More kilometres for each litre means the car travels further on the same fuel.
Watch the direction of the unit though: fuel consumption given the other way round, as litres per kilometre, is better when the number is smaller.
Complete the three speed relationships:
$speed = distance \div______, time = distance \div______and distance = time \times______$
The completed relationships are:
$speed = distance \div time, time = distance \div speed and distance = time \times speed$
Each one is a rearrangement of the first, so remembering that speed is a distance divided by a time is enough to rebuild the other two.
Why must you check the units before dividing a distance by a time?
Because the units of the answer come straight from the units you put in.
An answer in metres per second needs the distance in metres and the time in seconds, so a distance in kilometres or a time in minutes has to be converted first.
This is the commonest place marks are lost in this topic.
A runner completes a 10 km race in 45 minutes. What is the average speed in metres per second, to 3 significant figures?
The average speed is 3.70 metres per second.
Convert both quantities first: 10 km is 10 000 m, and 45 minutes is $45 \times 60 = 2700$ seconds.
Dividing gives $10000 \div 2700 = 3.7037 . . .$ , which rounds to 3.70.
A sprinter runs 100 m at an average speed of 8.85 metres per second. How long does it take, to two decimal places?
It takes 11.30 seconds.
Time is distance divided by speed, so $100 \div 8.85 = 11.299 . . .$
The units already match, since the distance is in metres and the speed is in metres per second, so no conversion is needed.
True or False?
3.7 metres per second and 13.3 kilometres per hour describe the same speed.
True.
They are the same speed written in different units, since 3.7 metres per second covers 13 320 metres in an hour.
The number attached to a speed means nothing on its own: the units have to be read with it.

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