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
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