### Video Transcript

Complete 0.011 multiplied by 0.15
blank 0.011 multiplied by 0.15, using is less than, is equal to, or is greater
than.

In this problem, we’re given two
multiplications. And both of them involve
multiplying two decimals together. We have 0.011 multiplied by
0.15. And we have 0.011 multiplied by
0.015. And in the middle of the two
calculations, we have a blank space. This is the part that we need to
complete. And we’re told to fill in the gap
using one of three symbols — is less than, we’d use this symbol if the first
statement is less than the second statement; is equal to, we’d use the equal sign if
both statements are worth the same; and is greater than, and we’d use this symbol if
the first statement is greater than the value of the second statement.

And we might look at this question
and think to ourselves that we need to work out both multiplications to be able to
compare them and then work out which symbol to put in the middle of them. And in a way, that is what the
question’s asking us to do. But the numbers that are involved
in this particular question are such that we can answer it really quickly without
even doing any maths. Let’s go through the really quick
way to answer the question. And then, after we’ve done that,
we’ll calculate both amounts and answer it the way it’s supposed to be answered.

Let’s start by looking very closely
at both multiplications. What do we notice about them? They both begin with the same
number, 0.011. Because both multiplication involve
multiplying 0.011 by another number, we just need to look at the other number and
decide which one’s larger and which one’s smaller. Whichever of the two second numbers
is larger will give a larger answer. In the first statement, 0.011 is
being multiplied by 0.15. That’s zero ones, one tenth, and
five hundredths. In the second calculation, 0.011 is
being multiplied by 0.015. Again, that zero ones. This time we have zero tenths, one
hundredth, and five thousandths.

So let’s compare the two numbers
that we’re multiplying 0.011 by. Both numbers have no ones. So we need now to compare the
tenths. The first number contains one
tenth, but the second number contains zero tenths. The first number then is larger
than the second number. Because both numbers are being
multiplied by the same number, 0.011, this means that the greater number will give
the greater answer. We don’t even have to work it
out. And so the correct symbol to use is
is greater than.

Let’s check our answer now, in
perhaps the way that the question was intended to be worked out. When we multiply two decimals
together, it’s often useful to ignore the decimal point and to think of the number
without a small point in it. In other words, that calculation
becomes 11 multiplied by 15. This isn’t just a trick. We’ve actually done something to
the numbers to turn them into 11 and 15. 0.11 has been multiplied by 1000;
the digits have moved three places to the left. That gets rid of the decimal
point. And 0.15 has been multiplied by
100. The digits have moved two places to
the left. so In total, the digits have moved five places to the left. They moved three places in the
first number and two places in the second number.

We’ll make a note of that because
once we’ve worked out the answer, we need to move the digits five places back again,
this time five places to the right. So first of all, let’s work
out. 11 multiplied by 15. We know 10 lots of 15 equals
150. So 11 lots of 15 is one more 15 on
top of that, which is 165. But remember, we altered our
numbers by moving them in total five places to the left. So we now need to look at the
number 165 and move the digits five places back again to the right. There’s 165 and we can shift them
once, twice, three times, four times, five times. The answer to our first
multiplication is 0.00165. Now, let’s work out the answer to
the second multiplication.

First, we can write down both
numbers without a decimal point in them. Remember again, this isn’t a trick
that we’ve used. What we’ve done is we’ve multiplied
both numbers. We’ve multiplied the first number
by 1000. We know this because it’s the same
numbers we used in the last one. The digits have moved three places
to the left and to get from 0.015 to 15 we’ve also multiplied by 1000. So we’ve moved the digits in that
number. Another three places to the
left. The digits have moved six places to
the left in total.

So again, once we’ve finished
working out the multiplication, we need to move them back again six places to the
right. The multiplication is exactly the
same, 11 multiplied by 15 equals 165. But this time, instead of moving their digits
five places to the right, we need to move them one more place to the right. So we can say that the answer is
definitely going to be 0.000165. And this is smaller than the first
number. The first number is greater than
the second number. And that’s how to prove that we
need to use the is greater than symbol.

We found the answer in two
ways. The second method we used was to
calculate both statements separately and to compare them to see which was the
larger. But the first method we used was a
lot quicker. We noticed that both statements
involved the same number to start with. So we just looked at the second
numbers, compared them and decided which was the larger. We knew that the statement with the
largest second number would have a larger total and a larger value. 0.011 multiplied by 0.15 is greater
than 0.011 multiplied by 0.015.