Video: AQA GCSE Mathematics Higher Tier Pack 2 • Paper 1 • Question 1

Which of these has the least value? Circle your answer. [A] 3.27 × 10⁻⁴ [B] 0.0000327 [C] 326.8 × 10⁻⁶ [D] 3.3 × 10⁻⁵.

04:24

Video Transcript

Which of these has the least value? Circle your answer. 3.27 multiplied by 10 to the power of negative four, 0.0000327, 326.8 multiplied by 10 to the power of negative six, or 3.3 multiplied by 10 to the power of negative five.

So when we take a look at these values, what we can see is that two of them are in standard form. And standard form is when we have a number 𝑎 multiplied by 10 to the power of a different number. So it’s multiplied by 10 to the power of some number.

Well, with that definition, that means that the third value should also be considered being in standard form because we’ve got a number 𝑎 multiplied by 10 to the power of another number. However, it’s not. And the reason it’s not is because our 𝑎 value must be between one and 10. And 326.8 is not between one and 10.

So therefore, to answer this problem, what I’m going to do is convert our second and third values into standard form. Well, for our second value to be converted, we’re gonna have 3.27. And that’s because this is between one and 10 and this is multiplied by 10 to the power of a number.

And to work out what number this is, we need to look at how many place values the three would have to move to the left to get to 3.27. And as I has to go to the left five spaces, we could say that it’s gonna be 10 to the power of negative five.

And we know that it’s going to be negative five because if we have a value that is less than one, so zero point something, then we know this can be multiplied by 10 to the power of a negative value. If it’s greater than one, so getting to the tens, hundreds, thousands, et cetera, then we know the power is going to be positive.

Now, if we take a look at our third value, we’ve got 326.8 multiplied by 10 to the power of negative six. So this time, we want our 𝑎 part of the value to be 3.268 cause again this is between one and 10. And then, we’ll need to find out what the power of 10 is going to be that we’re gonna multiply this by.

Well, this time, you can see that the three is going to move two place values to the right to make it from the hundreds to the units column. And therefore, what we need to do is add two to the power of 10 because we’re moving it two place values to the right to go from — as we said — the hundreds column to the units column.

So if we add two to negative six, we get to negative four. So therefore, we can say that 326.8 multiplied by 10 to the power of negative six in standard form is 3.268 multiplied by 10 to the power of negative four.

So now, in order to solve the problem, we want to work out which has the least value. Well, first of all, we can rule out the two values that have 10 to the power of negative four.

And that’s because if we’re looking for a least value, then a number that has 10 to the power of negative five is going to be less and that’s because negative five is more negative than negative four. So therefore, it’s gonna have more zeros before the first digit.

So now, we have two values that have the same power of 10 which is negative five. What we need to do is look at the first part, so the 𝑎 part in our standard form. So we’ve got 3.27 and 3.3.

Well, 3.3 is greater than 3.27 and that’s because 3.3 has three tens, whereas 3.27 only has two tens.

Don’t make the common error, which is to think “Well, it’s 3.27 and 27 is bigger than three,” because that’s not what it means. So therefore, as 3.3 is greater than 3.27, we can circle the least value which is 0.0000327.

And we know that’s the least value because when we’ve written it in standard form, it is 3.27 multiplied by 10 to the power of negative five, which is the least value out of all four values that we have.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.