+0

# decimal////

+1
180
1
+840

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

May 19, 2018

#1
+3855
+2

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 $$\boxed{7}$$

May 19, 2018