Estimation and Currency Conversion

Overview


Remem­ber that Esti­ma­tion and Cur­rency Con­ver­sion is part of Unit 2 and no cal­cu­la­tors are allowed. 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

1. 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.

2. Esti­mate:-

a)   (4.4 x 589)/(94 — 28)

b)   (87.6 x 6.2)/0.18

c)     8.3²/(1,236 ÷ 11.8)

3. Gatwick Air­port exchange rates UK Ster­ling (£) and Swedish Kro­ner (Skr) are as follows:-

Estimation and Currency Conversion £/Skt Table

 

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?

4. 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. Look at this table:-

Rounding to One Significant Figure

 

 

 

 

 

 

 

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

1. 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

2. 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

3 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.

4. 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.


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