Units, time and conversions

Learn

Metric units

The metric system works in powers of ten, and the prefix tells you the size. Kilo means 1,000 (1 kg = 1,000 g; 1 km = 1,000 m), centi means one hundredth (100 cm = 1 m) and milli means one thousandth (1,000 ml = 1 litre; 1,000 mm = 1 m; 10 mm = 1 cm).

To change to a smaller unit, multiply — there will be more of them: 2.4 kg = 2,400 g. To change to a larger unit, divide: 4,500 g = 4.5 kg. Before adding or comparing measurements, put them in the same unit, so 750 ml + 1.25 litres becomes 750 ml + 1,250 ml = 2,000 ml.

Time

Time is not decimal: there are 60 minutes in an hour, so 2.5 hours is 2 hours 30 minutes, and 7.75 hours is 7 hours 45 minutes. To find a duration, count on in stages — to the next whole hour, then whole hours, then the remaining minutes. A shift from 07:45 to 16:15 is 15 minutes to 08:00, 8 hours to 16:00, and 15 minutes more: 8 hours 30 minutes. Subtract any unpaid break afterwards.

Typing 2 hours 30 minutes into a calculator as 2.30 is a classic error; use 2.5. Divide minutes by 60 to turn them into a decimal part of an hour.

Metric and imperial (Level 2)

Imperial units such as miles, pounds, feet and gallons are still common in the UK. Questions will give you a conversion factor — for example 1 mile ≈ 1.6 km, 1 kg ≈ 2.2 lb, or 1 foot = 30.48 cm — and you multiply or divide by it. Decide which way by asking whether the answer should be a bigger or smaller number. Kilometres are shorter than miles, so a distance in km is the larger number.

A conversion graph is a straight line showing two units against each other. Read across from one axis to the line, then down or up to the other. For values beyond the graph, use proportion: if 10 gallons is about 45 litres, 4 gallons is about 18 litres.

Compound measures (Level 2)

A compound measure combines two units. Speed is distance ÷ time (km/h or mph); rearranged, distance = speed × time and time = distance ÷ speed. Density is mass ÷ volume (g/cm³). A rate of pay is money ÷ hours (£ per hour). The units of the answer tell you what to divide by what. Convert any minutes to hours first: 1 hour 30 minutes is 1.5 hours.

Level 1 typically covers metric conversions, time and the 24-hour clock. Level 2 adds imperial conversions, conversion graphs and compound measures.

Watch out

Common mistakes

• Treating time as decimal: 1 hour 30 minutes is 1.5 hours, not 1.3.
• Multiplying when you should divide in a conversion. Check whether the answer should be bigger or smaller.
• Adding measurements in different units, such as millilitres and litres, without converting.
• Mixing minutes and hours in a speed calculation.

Real life

Where you'll use this at work or home

• Working out paid hours on a timesheet and planning shift patterns.
• Converting recipe measures, or the weight of luggage in pounds and kilograms.
• Estimating journey times from distance and average speed.
• Comparing hourly rates of pay between two jobs.