The skills learned here are very useful in real life and you should be able to think of many day to day applications.
Here are some questions with the approach explained and finally the answers.
Estimation and Currency Conversion Questions
- It is 160 miles from Ipswich to Southampton. Paul’s car averages 6.4 miles for each litre of petrol. Currently Paul has 29 litres of petrol in his car. Estimate whether Paul has enough petrol in his car to drive from Ipswich to Southampton.
a) (4.4 x 589)/(94 — 28)
b) (87.6 x 6.2)/0.18
c) 3²/(1,236 ÷ 11.8)
- Gatwick Airport exchange rates UK Sterling (£) and Swedish Kroner (Skr) are as follows:-
Mr. Eriksson is traveling to Sweden to scout for talent. At Gatwick Airport he exchanges £1,500 into Swedish Kroner. In Sweden he spends Skr 9,300 in cash. On his return to his Gatwick he exchanges his remaining Swedish Kroner (Skr) back to UK Sterling £.
a) How many Swedish Kroner did Mr. Eriksson receive when he exchanged his £1,500?
b) When he returned to Gatwick how many UK pounds did he receive in exchange for his remaining Swedish Kroner?
c) Why are there different rates to exchange from, and into UK Sterling?
- After completing his scouting trip to Sweden, Mr. Eriksson (manager of Leicester City in the UK) has to make a decision. He has looked at 3 players who are available at the following transfer fees:
Player A (from Sweden) who is available at Skr 7,788,000
Player B (from France) who is available at €840,000
Player C (from USA) who is available at $1,280,000
The exchange rates for these purchases are £1 = Skr11.0, £1 = €1.20 and £1 = $1.60.
Mr. Eriksson thinks that all 3 players are very similar and decides he will buy the cheapest player. Which player should be buy?
Estimation and Currency Conversion Approach
1 & 2. Remember that in this section your are not allowed to use a calculator. It helps if you are confident about your times tables including the 11 times table and the 12 times table.
When you are estimating a calculation, the key is to round all the numbers within the calculation to one significant figure. What does this mean? When you have a number between one and ten, round to the nearest whole number. When you have 2 digit number, round to the nearest ten. When you have a 3 digit number round to the nearest hundred etc etc.
So, to round to one significant figure, you work from the left and round to the first digit (nb if the number is 0.76543 you round to the “7” and not the “0” as the zero is only written to make the number easier to read). For more practice rounding try BBC GCSE Bitesize: Rounding and Estimating
Once you have rounded each number within the calculation to one significant number you use your arithmetic skills (remember no calculator) to work out the answer.
3 & 4. Currency conversion questions are usually not difficult. You are given the exchange rate so it is just a matter of working through the question carefully and making sure you do the conversion “the right way round”. It would help to practice a few questions and make yourself familiar with the most common currencies (Euro’s, US Dollars, Swedish Kroner etc).
Estimation and Currency Conversion Answers
- Estimate for the distance that Paul can expect to travel using the petrol he has ≈
6 (rounded to one significant figure from 6.4) x 30 (rounded to 1 s.f. from 29) = 180 miles.
As it is only 160 miles to Southampton he should have enough petrol to drive his car from Ipswich to Southampton
- a) Rounding to 1 s.f ≈ (4 x 600)/(90–30) = 2,400/60 = 4.0
b) ≈ (90 x 6)/0.2 = 540/0.2 (multiply top and bottom of sum by 10 to convert 0.2 to whole number) = 5,400/2 =2,700.
c) 8.3²/(1,236 ÷ 11.8) ≈ 8 x 8/(1,200 ÷ 12) = 64/100 = 0.64
- a) £1,500 x 11 = Skr 16,500
b) He has Skr 16,500 — Skr 9,300 = Skr 7,200 remaining
Skr 7,200 / 12 = £600
c) The difference in exchange rates is to allow the bank offering the service to make a profit.
- Converting all the fees to UK pounds (£) we get.
Player A = Skr 7,788,000/ 11 = £708,000
Player B = €840,000/1.2 = 8,400,000/12 = £700,000
Player C = $1,280,000/1.6 = 12,800,000/16 = £800,000
So the cheapest player is player B from France.