Loading [MathJax]/jax/output/SVG/jax.js

Number Theory

0

15

1

+1926

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$

tomtom Jun 17, 2024

Best Answer

+1946

+1

Let's first take a look at the fraction 1/17.

It has 16 repeating digits in the form of $0. \overline{0588235294117647}$

We simplfy have to find which digit the 4000th lies on.

First, let's do 4000/16.

We get

$4000/16=250$

So the 4000th digit is the last digit of the repeating decimal, which is 7.

So 7 is our answer.

Thanks! :)

NotThatSmart Jun 17, 2024

1⁺⁰ Answers

+1946

+1

Best Answer

Let's first take a look at the fraction 1/17.

It has 16 repeating digits in the form of $0. \overline{0588235294117647}$

We simplfy have to find which digit the 4000th lies on.

First, let's do 4000/16.

We get

$4000/16=250$

So the 4000th digit is the last digit of the repeating decimal, which is 7.

So 7 is our answer.

Thanks! :)

NotThatSmart Jun 17, 2024

2 Online Users