Video Transcript
Find the value of the product of 20
times three-quarters times 0.18 to the nearest two decimal places.
In this question, we are asked to
evaluate the product of three rational numbers and give our answer to the nearest
two decimal places.
To answer this question, we can
start by recalling that the multiplication of rational numbers is associative and
commutative. So, we can rearrange the product
and evaluate the product in any order. Next, we can also recall that it is
often easiest to multiply rational numbers together when they are all written as
fractions.
So, we will start by writing all of
the factors as fractions. It is not necessary to rewrite 20
as 20 over one, since 20 will just be a factor in the numerator. However, we will convert
anyway. We can also note that 0.18 is equal
to 18 over 100 to obtain the following product. We can now multiply the fractions
by recalling that we multiply two fractions by multiplying their numerators and
denominators together separately.
In general, we could multiply
fractions by recalling that 𝑎 over 𝑏 times 𝑐 over 𝑑 is equal to 𝑎𝑐 over
𝑏𝑑. This result extends to the product
of any number of fractions. So, we have 20 times three times 18
divided by one times four times 100. We could now evaluate the products
in the numerator and denominator. However, it is easier to cancel the
shared factors first. We can see that there is a shared
factor of four in the numerator and denominator. We can cancel this factor as
shown.
We could now continue to cancel
shared factors. However, we are told to give our
answer to two decimal places. We know that a fraction with a
denominator of 100 is easy to convert into a decimal. So, we will leave the denominator
as 100. Evaluating the product in the
numerator, we have that five times three is 15. And then we can calculate that 15
times 18 is equal to 270. So, we have 270 divided by 100.
We can then convert 270 over 100
into a decimal by moving the decimal point over two spaces to the left to obtain
2.70. It is worth noting that the exact
value of this product is 2.7. However, since we are asked for two
decimal places of accuracy, we will give the answer of 2.70.
