### Video Transcript

Complete nine hundred and forty-seven divided by nought point eight nine is something
to nine hundred and forty-seven divided by eight point nine times nought point
nought one using the less than sign, the equal to sign, or the greater than
sign.

So we’ve got two different expressions and we’ve got to decide which one is bigger
than the other. Now if I can rearrange the expression on the right-hand side so that it contains
exactly the same expression on the left-hand side but multiplied or divided by
something, that will help me to decide which is the bigger expression.

Well in fact to make my life easier, before I start I’m going to reexpress the
left-hand side: nine hundred and forty-seven divided by nought point eight nine can
be rewritten as nine hundred and forty-seven over nought point eight nine.

So now let’s do a similar thing to the right-hand side: nine hundred and forty-seven
divided by eight point nine can be rewritten as nine hundred and forty-seven over
eight point nine, and of course that’s got to be multiplied by nought point nought
one.

Now nought point nought one has got a one in the hundredths column, so that means one
hundredth. So I’m going to write this as, instead of nought point nought one, I’m gonna write it
as one hundredth, one over a hundred.

Now these two terms here look quite a lot like each other. We’ve got nine hundred and forty-seven over zero point eight nine, and we’ve got nine
hundred and forty-seven over eight point nine. Now I’m gonna reexpress eight point nine as nought point eight nine times ten; if I
multiply nought point eight nine by ten, I get eight point nine.

And because I’m multiplying two fractions together on this right-hand side over here,
it doesn’t matter whether I do the multiplying by ten over here or if I move it to
over here, and that’s what I’m gonna do.

And now I’ve got nine hundred and forty-seven over nought point eight nine here, and
I’ve got nine hundred and forty-seven over nought point eight nine here. But in this case, I’m multiplying it by one over a hundred times ten, or one over a
thousand.

So we’ve got the same expression or the same term here and here, but on the
right-hand side, we’re gonna take that expression and multiply it by a thousandth or
divide by a thousand; we’re gonna make it smaller. So that’s gonna be the smaller number, and this one is gonna be the bigger
number.

So we can write our sign this way round: nine hundred and forty-seven divided by
nought point eight nine is greater than nine hundred and forty-seven divided by
eight point nine times nought point nought one. So there we have our answer.