Money
Calculating with money, from shopping and change to wages, salaries and household bills, and converting between currencies using an exchange rate. You will see when to round to the nearest cent or penny, and when a money answer must be rounded down instead.
What the syllabus says
C1.16 (Core)
- 1 Calculate with money.
- 2 Convert from one currency to another.
E1.16 (Extended)
- 1 Calculate with money.
- 2 Convert from one currency to another.
Quoted from the Cambridge IGCSE Mathematics 0580 syllabus for 2025 to 2027.
Money and its units
Most currencies split into 100 smaller units: 100 pence (p) make £1, and 100 cents make 1 euro or 1 dollar. So:
- to change pence into pounds, divide by 100: 465p ;
- to change pounds into pence, multiply by 100: £0.08 p.
An amount of money is written with two decimal places: £4.50, not £4.5, and €12.00 or €12, never €12.0. The two decimal places are the pence or cents.
Without a calculator, line up the decimal points when you add or subtract, and when you multiply it is often easier to work in pence: is p, which is £4.05.
When a calculation gives more than two decimal places, round to the nearest penny or cent, which is 2 decimal places: £18.547 becomes £18.55. Only round the final answer, never part-way through.
Sometimes the context decides the rounding instead:
- "How many can she afford?" means round down: with £20 and tickets at £6, she can buy 3, not and not 4.
- "How many packs must he buy?" means round up: if he needs 7 rolls and they come in packs of 4, he must buy 2 packs.
Worked example 1
Lena buys 2 drinks at £1.45 each and a sandwich at £3.80. She pays with a £10 note. How much change does she get?
Drinks: , so £2.90.
Total: , so £6.70.
Change: count up from £6.70. 30p takes it to £7.00, then £3 takes it to £10.00.
Change .
Answer: £3.30
Check yourself
Tom buys 4 tins of soup at 85p each and a loaf of bread for £1.35. He pays with a £5 note. How much change does he get? Give your answer in pence.
Answer it in the portal, where your answer is checked as you type →
Wages, salaries and bills
Wages. Pay for each hour worked is a rate: pay hours worked rate per hour. Extra hours often earn overtime:
- "time and a half" means the normal rate;
- "double time" means the normal rate.
Work out the normal pay and the overtime pay separately, then add.
Salaries. A salary is pay for a year. Divide by 12 for the pay each month, or by 52 for the pay each week. To find an hourly rate from a salary, divide by the total number of hours worked in the year.
Bills. Gas, electricity and water bills usually have two parts:
- a standing charge, a fixed amount for each day, paid however little you use;
- a charge for each unit used. The units used are the difference between two meter readings: present reading minus previous reading.
Prices on bills are often in pence, and the total is in pounds. Convert before you add, or the answer will be 100 times too big.
Worked example 2
An electricity meter reads at the start of a quarter and at the end. Each unit costs 27.6p, and there is a standing charge of 53p per day for 92 days. Calculate the total bill, correct to the nearest penny.
Units used: .
Cost of units: p, which is £185.472.
Standing charge: p, which is £48.76.
Total: , so the bill is £234.23 to the nearest penny.
Notice that the rounding is done only once, at the end.
Answer: £234.23
Converting between currencies
An exchange rate tells you how much of one currency you get for one unit of another. For example, £1 = €1.16 means every pound is worth 1.16 euros.
- Pounds to euros: each pound becomes 1.16 euros, so multiply by 1.16. £250 is .
- Euros to pounds: reverse the process, so divide by 1.16. €75 is , which is £64.66 to the nearest penny.
Always do a sense check. Here a euro is worth less than a pound, so the number of euros should be bigger than the number of pounds it came from. If your conversion makes the number smaller, you have multiplied when you should have divided, or the other way round.
If you are unsure which operation to use, write the rate as a ratio line and scale it:
To compare prices in two countries, convert one price into the other currency so that both are in the same units, then compare. Banks and exchange bureaux sometimes also charge a fixed fee, or use one rate when they sell a currency and a different rate when they buy it back; a question will tell you exactly how.
Worked example 3
The exchange rate is 1 US dollar = 0.92 euros. (a) Change 400 dollars into euros. (b) Change 230 euros into dollars.
(a) Dollars to euros: multiply by the rate. euros.
Sense check: a dollar is worth a little less than a euro here, so 400 dollars gives a slightly smaller number of euros. 368 is sensible.
(b) Euros to dollars: divide by the rate. dollars.
Non-calculator method for (b): .
Answer: (a) 368 euros (b) 250 dollars
Worked example 4
A pair of trainers costs £84.00 in London and €99.00 in Madrid. The exchange rate is £1 = €1.16. In which city are the trainers cheaper, and by how much in pounds?
Convert the Madrid price into pounds so both prices are in the same currency: , so £85.34.
London: £84.00. Madrid: £85.34.
Difference: , so £1.34 to the nearest penny.
The trainers are cheaper in London, by £1.34.
Answer: London, by £1.34
Check yourself
The exchange rate is 1 euro = 1.085 US dollars. Change 340 dollars into euros. Give your answer correct to the nearest cent.
Answer it in the portal, where your answer is checked as you type →
Key points
100 pence = £1 and 100 cents = 1 euro or 1 dollar. Money is written to 2 decimal places.
Round money to the nearest penny or cent only at the end. "How many can I afford?" rounds down; "how many must I buy?" rounds up.
Overtime at time and a half is the normal rate. A salary is per year: divide by 12 for monthly pay.
A bill is standing charge plus units used times price per unit. Units used = present reading minus previous reading.
With £1 = €: pounds to euros multiply by , euros to pounds divide by . Check the size of your answer makes sense.
To compare prices, convert to the same currency first.
Where marks are lost
Writing £4.5 instead of £4.50, or giving £18.547 when the answer should be to the nearest penny.
Adding pence to pounds: 85p plus £1.35 is £2.20, not £86.35.
Multiplying when you should divide in a currency conversion. Use the sense check every time.
Rounding up when the question asks how many you can afford, or down when it asks how many you must buy.
Paying overtime hours at the overtime rate and then also at the normal rate, or using the total hours.
Forgetting the standing charge on a bill, or subtracting the meter readings the wrong way round.
Rounding an earlier answer and using the rounded value later, which can change the final penny.
Related IGCSE Mathematics 0580 lessons
An original lesson written to the Cambridge IGCSE Mathematics 0580 syllabus (2025 to 2027). The worked examples and questions are our own, not Cambridge questions. Back to every IGCSE Mathematics 0580 lesson.