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what is the 42nd digit after the expansion of 1/27? 

 May 19, 2018
 #1
avatar+4083 
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Nice to meet you again, Ant!

We first find the value of 1/27 and see if it repeats.

 

\(\frac{1}{27}=0.0370370\). This number repeats forever.

If you see closely, only the 0, 3, and 7 repeats. This is 3 numbers.

If we want the 42nd digit, we simply divide 42 by 3 to get 14.

We're are not done, yet! The question is asking us to find what digit!

Since 3 goes into 42 evenly, with a remainder of 0, we look at the last digit of our repeating trio.

Remeber, R1= First number, and R0= Last Number

Thus, the answer is \(\boxed{7}\)

 

smileysmiley

 May 19, 2018

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