Video: AQA GCSE Mathematics Higher Tier Pack 4 • Paper 3 • Question 11

Write down possible values of 𝑟, 𝑠, and 𝑡 for the following equation to be true: (2.5 × 10^𝑟) + (2.5 × 10^𝑠) + (2.5 × 10^𝑡) = 2525.025.

03:30

Video Transcript

Write down the possible values of 𝑟, 𝑠, and 𝑡 for the following equation to be true: 2.5 multiplied by 10 to the power of 𝑟 plus 2.5 multiplied by 10 to the power of 𝑠 plus 2.5 multiplied by 10 to power of 𝑡 equals 2525.025.

So as we can see, we want to break up 2525.025 into three parts and each of these are standard form involving the decimal 2.5. So in order for us to work this out, what I’m going to do is I’m going to split up 2525.025 into three parts, each where the first two significant figures are two five. So when I do that, I get 2525.025 is equal to 2500 plus 25 plus 0.025.

So as you can see, we’ve got our first two significant figures in each case are 25. It is worth noting though that in 0.025, the two five is the first two significant figures because the two is the first nonzero digit. So now, what we’re gonna do is rewrite each part in standard form. So in this example, what I’m going to do is I’m going to relate the 2.5 multiplied by 10 to the power of 𝑟 to 2500.

So we’ve got 2500 is equal to 2.5 multiplied by 10 to the power of three. And we’ve got multiplied by 10 to the power of three because if we think about the 2.5, that’s two in the units column and five in the tenths column. And if we wanted to convert 2.5 to 2500, then we’d have to move each digit three spaces, so three place values to the left. So that’s why we multiply it by 10 to the power of three. So therefore, we can say the value of 𝑟 that we’d work would be three.

Okay, let’s move on to the next part. Well for the next part, which is the 2.5 multiplied by 10 to the power of 𝑠, we’re gonna represent this using the 25. So 25 is equal to 2.5 multiplied by 10 or 10 to the power of one. We don’t usually write that one. And again, using our place values, we can see the reason this would be is because the two from 2.5 would move one place value to the left to go to 25 and the same for the five that would move one place value to the left. So we’ve got 2.5 multiplied by 10 to the power of one or 10.

So therefore, a value for 𝑠 that’s gonna work for us is 𝑠 is equal to one. And then finally, we have 0.025. Well, this is equal to 2.5 multiplied by 10 to the power of negative two. So it’s gonna be negative two because first of all we’re moving two place values to the right this time not the left. Also, it’s worth noting that if we have a value that is less than one, then this is going to be a negative power of 10. So therefore, we can say a value of 𝑡 that’s gonna work is gonna be negative two.

So therefore, we can say the three possible values of 𝑟, 𝑠, and 𝑡 are 𝑟 is equal to three, 𝑠 is equal to one, 𝑡 is equal to negative two. These could also be interchanged.

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