Number - Measures and accuracy: use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate

The idea

The units the exam expects include grams, kilograms and tonnes for mass; millimetres, centimetres, metres and kilometres for length; seconds, minutes and hours for time; pounds and pence for money; and litres and millilitres for capacity. A compound measure divides one quantity by another, and the two need not both come from that list: speed = distance ÷ time, density = mass ÷ volume, and pressure = force ÷ area, each rearranging to give whichever quantity is missing. A car covering 150 km in 2 hours has a speed of 150 ÷ 2 = 75 km/h. Make the units agree before you calculate, because a speed in km/h needs a time in hours, so 2 hours 30 minutes is 2.5 hours and not 2.3 hours. Decimal quantities are normal here, so 1250 g is 1.25 kg. Write the unit beside every answer, since a bare number is not a measure and a compound measure carries a compound unit such as g/cm³.

What earns the marks

• A correct conversion into consistent units before the calculation, such as minutes turned into hours.
• The correct compound formula quoted or used in a rearranged form.
• The substitution into that formula, even if the arithmetic that follows is wrong.
• The final value with the correct unit attached, including the compound unit where one is needed.

Common mistakes and how to put them right

• Writing 2 hours 45 minutes as 2.45 hours rather than 2.75 hours.

• Using the length conversion factor once for square units, so treating 1 m² as 100 cm² when it is 10000 cm².

• Mixing units inside one calculation, such as a distance in metres with a time in hours.

• Rearranging the speed formula wrongly and dividing time by distance.

Exam tips

• Write the units in your working line by line; a unit that does not cancel sensibly is a warning that a conversion is missing.
• Convert a time to hours as a decimal whenever the speed is in kilometres or miles per hour, and remember that sixty minutes make an hour, not a hundred.
• Sanity check the size of the answer, since a walking pace of 500 km/h is telling you a conversion went wrong.