Video: AQA GCSE Mathematics Higher Tier Pack 5 • Paper 3 • Question 9

The table below shows data about the amount of rain that fell on a particular day in February in two cities. The rainfall during this particular day can be found using the following formula. Rainfall = total volume of rain/area. Compare the rainfall of Cambridge and Seattle.

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Video Transcript

The table below shows data about the amount of rain that fell on a particular day in February in two cities. The two cities that we’re comparing are Cambridge and Seattle. It shows the area of the city in square metres and the total volume of rain in cubic metres. The rainfall during this particular day can be found using the following formula. Rainfall is equal to the total volume of rain divided by the area. Compare the rainfall of Cambridge and Seattle.

So we’re asked to compare the rainfall between the two cities. And we are given a formula to find the rainfall. We need to take the total volume of rain, which can be found in this column, and divide it by the area, which can be found in this column.

So let’s begin with Cambridge. To find the Cambridge rainfall, we need to take the 3680 cubic metres, which is the total volume of rain for Cambridge, and divide by the area of the city, 115 million square metres.

Let’s first look at our units. We have cubic metres on the top and square metres on the bottom. So square metres means we have metre times metre, which is how we get square metres. Metres cubed means we have metres times metres times metres. So the two metres that are on the bottom can cancel with two of the metres that would be at top, which would just leave metres, which makes sense. Rainfall should be in metres. So if we would divide these numbers, we will get 0.000032 metres.

Now let’s look at the rainfall in Seattle. We take its total volume of rain, which is 6293 cubic metres, and divide by the area of the city, which is 217 million square metres. Once again, our units will be in metres. And we get 0.000029 metres.

Now we are asked to compare the rainfall between the two cities. So let’s compare these two numbers that we got. The nice part is, is that even though these decimals are very small, the zeros line up. So we can really compare the 32 and the 29. 32 is larger, so this means that there was more rainfall in Cambridge than Seattle.

But let’s go ahead and compare these numbers in a different way. How about we convert these numbers to standard form so maybe it’ll be a little easier to compare the numbers? To convert to standard form, we need to make these numbers to be between one and 10, where it could be equal to one, but it has to be less than 10. This would require moving our digits to the left five spaces.

So that way, we would create the number 3.2. So we would have 3.2 times 10 to the power of negative five. So we can think of this two ways. If we move the digits to the left, the exponent, the power, needs to be negative, hence a negative five. Or we can think, if we have tiny numbers that are less than one, our power needs to be negative.

So for the rainfall in Seattle, we will need to do the same thing. The digits would need to move five spaces to the left. And we would create 2.9. So we would have 2.9 times 10 to the power of negative five metres. Both of these numbers are multiplied by 10 to the power of negative five. So we can compare 3.2 and 2.9. 3.2 is larger. So that means that there was more rainfall in Cambridge compared to Seattle. So once again, our final answer would be that there was more rainfall in Cambridge than Seattle.

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