Video Transcript
How many times larger is six
multiplied by 10 to the fifth power than two multiplied by 10 to the third
power?
When we’re asked how many times
larger one number is than another number, we can think of this as what would we need
to multiply the smaller number by to get the bigger number. So, dividing the larger number by
the smaller number will give us what we’re looking for.
Notice that in this question these
numbers may look a little different. That’s because these numbers are
given in scientific notation. This means they have been written
in the form 𝑎 multiplied by 10 to the 𝑛th power, where the absolute value of 𝑎 is
greater than or equal to one and less than 10 and 𝑛 is an integer. But the important thing to remember
is that they are both just numbers, although we do divide them in a slightly
different way. We could convert them both to not
be in scientific notation, but then we would be working with two very large
numbers. So we’re going to keep them in
their scientific notation and divide them.
Let’s begin by writing the division
in this way: six multiplied by 10 to the fifth power over two multiplied by 10 to
the third power. This can then be written as a
multiplication of two fractions. Six over two multiplied by 10 to
the fifth power over 10 to the third power. We can then calculate each of these
two fractions separately. Six over two is three. Then, to calculate 10 to the fifth
power over 10 to the third power, we use the exponent quotient rule. That is, 𝑥 to the 𝑚-power over 𝑥
to the 𝑛-power equals 𝑥 to the 𝑚 minus 𝑛 power. So, 10 to the fifth power over 10
to the third power is 10 to the five minus three power. As five minus three is two, we
therefore have three multiplied by 10 to the second power.
So, we could say that six
multiplied by 10 to the fifth power is three multiplied by 10 squared times larger
than two multiplied by 10 to the third power. But generally we wouldn’t quite
word it in this way. So let’s take our answer of three
multiplied by 10 to the second power out of scientific notation. So let’s actually calculate three
multiplied by 10 squared. 10 squared just means 10 multiplied
by 10, and we know that’s 100. So we have three multiplied by 100,
which is 300.
So, we conclude that six multiplied
by 10 to the fifth power is 300 times larger than two multiplied by 10 to the third
power.
