How do you simplify and make the fraction 4/33 into a decimal?

1 Answer
Oct 4, 2015

Answer:

You can long divide #4# by #33# and observe the repeating remainder, or simply notice that #4/33 = 12/99 = 0.121212... = 0.dot(1)dot(2)#

Explanation:

First note that #4# and #33# have no common factor greater than #1#, so #4/33# is already in simplest form.

When we start to long divide #4# by #33# it only takes a couple of digits to get back to the number we first started with...

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So we get a repeating decimal expansion:

#4/33 = 0.121212... = 0.dot(1)dot(2)#

Alternatively, note that #4/33 = (3*4)/(3*33) = 12/99 = 0.dot(1)dot(2)#