In a competition, a prize is won every 2014 seconds. Work out an estimate for the number of prizes won in 24 hours. You must show your working. (4 marks)

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They key to answering this question is that it is only asking for an estimate. So you don't need to provide an exact answer; as long as your answer is within a certain range you will get full marks provided that you show all your working.

To start you need to figure out roughly how many seconds there are in 24 hours. You know that in each hour there are 60 minutes and that in each minute there are 60 seconds. This means that in 24 hours you have 24 x 60 x 60 seconds. As this question comes up in a non-calculator paper you will have to work this out yourself. The easiest way is to round the 24 to 20, and you are allowed to do this since you only want an estimate. Now all you have to work out is 20 x 60 x 60 which looks a lot easier. If you ignore the zeros for now you can simply do 2 x 6 x 6 which is equal to 2 x 36 which again is equal to 72. Now you have to add the 3 zeroes that you removed earlier. So the answer to 20 x 60 x 60 is 72000. You have just worked out that there are roughly 72000 seconds in 24 hours (or a day).

The question states that there are prizes won every 2014 seconds. So to figure out how many prizes are won in 24 hours you need to find out how many times 2014 fits into 72000, or in other words 72000 / 2014. Once again you can make this division a lot easier by rounding the 2014 to 2000. Now you have 72000 / 2000. A neat trick to dividing is that if both the numerator and denominator have triailing zeroes you can remove a the last zero from both numbers until either one of the numbers no longer has a zero as its last digit. So step by step the above division would become 7200 / 200, then 720 / 20 and finally 72 / 2. So the answer to the question is 36. (which is half of 72).

Sivarjuen R. GCSE Maths tutor, 13 plus  Maths tutor, GCSE Physics tutor

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