What is the 2020th digit to the right of the decimal point in the decimal expansion of (3)/(7)? A) 1 B) 2 C) 4 D) 5 E) 8

Question

What is the 2020th digit to the right of the decimal point in the decimal expansion of


`(3)/(7)`?

A) 1
B) 2
C) 4
D) 5
E) 8

Answer 1

5

Explanation:

`(3)/(7)=0.\overline{428571}`

The period is 6.

The first digit to the right is 4.

The second digit to the right is 2.

Third digit to to the right is 8.

Fourth digit to the right is 5.

Fifth digit to the right is 7.

Sixth digit to the right is 1.

Then it starts over again.

The seven digit is 4. (Keep in mind 7=6+1).

The eight digit is 2. (Keep in mind 8=6+2).

So on...

So you can find the digit by finding the remainder of the nth digit to the right divided by 6 (since the pattern repeats the same 6 digits each time).

2020=6(336)+4

So the remainder is 4 since 2020/6=336+4/6.

Since the remainder is 4:

"Fourth digit to the right is 5".

The answer is 5.