0580 · 5.1Units of measure

Length, mass and capacity conversions

0:00A tank labelled one cubic metre can hold one thousand litres, not just one litre. A square metre contains ten thousand square centimetres, even though a metre contains only one hundred centimetres. These differences come from what we are measuring. By the end of this video, you will understand how to convert lengths, areas, volumes, capacities and masses without guessing the conversion factor. A measurement combines a number with a unit.

0:24The number tells us how many units we have, while the unit tells us the size of each piece. Converting units changes how we describe a quantity, not the quantity itself. A ribbon does not become longer when we express its length in millimetres rather than centimetres. Think of measuring as counting equal pieces. Smaller pieces require a larger count to describe the same amount, while larger pieces need fewer.

0:48This explains why we multiply when converting into smaller units and divide when converting into larger units. Length measures distance in one direction, such as the height of a door. Area measures the amount of surface covered, such as a floor. Volume measures the space occupied by something, while capacity describes how much a container can hold. Mass measures the amount of matter in an object and is measured here in grams or kilograms.

1:11For length, one centimetre equals ten millimetres, and one metre equals one hundred centimetres. That also makes one metre equal to one thousand millimetres. One kilometre contains one thousand metres. For mass, one kilogram equals one thousand grams. Capacity follows the same pattern, with one thousand millilitres in every litre. Choose units that suit the situation. Millimetres are useful for the thickness of a small object, while kilometres suit distances between towns.

1:40Grams suit the mass of a small packet, and kilograms suit a heavy bag. Millilitres are convenient for a small drink, while litres suit larger quantities of liquid. Our first exam-style example asks us to convert two point three five kilometres to metres, and seven hundred and fifty grams to kilograms. Each kilometre contains one thousand metres. We therefore calculate 2.35 × 1000, which gives two thousand three hundred and fifty.

2:07The length is two thousand three hundred and fifty metres. For the mass conversion, kilograms are larger units than grams. We divide seven hundred and fifty by one thousand, giving zero point seven five. The mass is zero point seven five kilograms. Both answers make sense because the smaller length unit gives a larger number, while the larger mass unit gives a smaller number.

Converting square units

2:28Area needs a different conversion factor because it involves two directions. A square metre is the area of a square with sides one metre long. Each side is one hundred centimetres long. Imagine filling it with small squares whose sides are each one centimetre long. There are one hundred small squares across and one hundred rows down. Multiplying one hundred by one hundred gives ten thousand small squares. Each small square has an area of one square centimetre.

2:56Therefore, one square metre equals ten thousand square centimetres, not one hundred. The general rule is to square the length conversion factor when converting area. Ten millimetres make one centimetre, so one square centimetre equals one hundred square millimetres. For the largest unit, squaring one thousand shows that a square kilometre holds one million square metres. The factor changes because both directions must be converted. Our second exam-style example asks us to convert thirty-six thousand square centimetres to square metres.

3:28One square metre contains ten thousand square centimetres. We divide thirty-six thousand by ten thousand, obtaining three point six. The answer is three point six square metres because we are counting larger units of area. Dividing by one hundred instead would give three hundred and sixty square metres. That would use a length conversion factor for an area. The original surface has not changed, so our conversion must account for both directions.

3:53This is why the word square matters as much as the unit name.

Converting cubic units

3:57Volume involves three directions: length, width and height. A cubic metre is the volume of a cube whose edges are each one metre long. In centimetres, each edge measures one hundred. Imagine filling that space with small cubes whose edges are each one centimetre long. One horizontal layer contains 100 × 100, giving ten thousand small cubes. There are one hundred such layers. Multiplying ten thousand by one hundred gives one million.

4:25Therefore, one cubic metre equals one million cubic centimetres. For volume, cube the corresponding length conversion factor. Since one centimetre equals ten millimetres, one cubic centimetre equals one thousand cubic millimetres. A metre is one thousand millimetres long, and cubing that factor makes a cubic metre equal to one billion cubic millimetres. These large factors come from converting all three directions, not from an arbitrary rule. Our third exam-style example asks us to convert twenty-four thousand cubic millimetres to cubic centimetres.

4:58One cubic centimetre contains one thousand cubic millimetres. Dividing twenty-four thousand by one thousand gives twenty-four. The answer is twenty-four cubic centimetres, with the cubic unit retained because we are still measuring volume.

Capacity, volume and unit checks

5:12Capacity and volume can describe the same amount of space using different units. The key connection is that one cubic centimetre equals one millilitre. One litre is one thousand millilitres. So one litre is also one thousand cubic centimetres. These relationships let us move between cubic units and liquid capacity units. We already know that one cubic metre contains one million cubic centimetres. That corresponds to one million millilitres. Dividing one million by one thousand gives one thousand litres.

5:43Therefore, converting cubic metres to litres means multiplying by one thousand, while converting litres to cubic metres means dividing by one thousand. An exam-style question gives a tank capacity of zero point three six cubic metres. The tank already contains two hundred and seventy-five litres. We must calculate how much additional water is needed to fill it. First, convert the total capacity into litres so both quantities use the same unit.

6:09Multiply zero point three six by one thousand to obtain three hundred and sixty. The tank can therefore hold three hundred and sixty litres. Subtract two hundred and seventy-five from three hundred and sixty to get eighty-five. The additional water needed is eighty-five litres. A common mistake is subtracting the original numbers before making their units match. That calculation would compare cubic metres with litres, which are differently sized units.

6:34Another mistake is treating litres as a mass measurement. Litres measure capacity, and you cannot convert them directly into kilograms without further information about the substance. These conversions must work without a calculator on Paper Two, as well as with a calculator on Paper Four. Write the unit relationship first, then choose multiplication or division. The conversion factors are exact, so the answers in these examples do not need rounding.

6:59For other calculated answers, follow the stated accuracy or the usual three significant figures, and avoid rounding intermediate values. The central idea is that changing units changes the count, not the quantity. Smaller units give larger numbers, and larger units give smaller numbers. Length uses the length conversion factor directly, area uses its square, and volume uses its cube. Always identify what is being measured before choosing your factor. Keep the capacity connections separate and clear.

7:28One cubic centimetre equals one millilitre, and one cubic metre equals one thousand litres. Use matching units before comparing, adding or subtracting measurements. With those ideas, unit conversion becomes a reasoned calculation rather than a rule you have to guess.