Video Transcript
Find 0.9 divided by one and
one-ninth. Give your answer as a decimal.
In this question, we are asked to
divide two rational numbers, one given as a decimal and the other given as a mixed
number. We need to give our answer as a
decimal. There are many ways that we could
answer this question. Of course, we could use a
calculator. However, we will go through a
method that works without a calculator.
The first thing that we want to do
is to write both numbers in the same form to make the division easier. In fact, it is usually easiest to
write both numbers as fractions when dealing with multiplication or division. We know that 0.9 is
nine-tenths. And we can rewrite the mixed number
as 10 over nine to obtain nine-tenths divided by ten-ninths.
Now that we have the division of
two fractions, we can recall that dividing by a fraction is the same as multiplying
by its reciprocal. In general, we have that 𝑎 over 𝑏
divided by 𝑐 over 𝑑 is equal to 𝑎 over 𝑏 times 𝑑 over 𝑐, provided that we are
not dividing by zero. Therefore, instead of dividing by
10 over nine, we can instead multiply by its reciprocal, nine over 10. We can then multiply the two
fractions by multiplying their numerators and denominators separately. We obtain nine times nine over 10
times 10. Evaluating these products gives us
81 over 100.
Remember though, we need to give
our answer as a decimal. We can do this by recalling that
dividing by 100 moves the decimal point two places to the left. So 81 over 100 is equal to
0.81.
