Question

What are the first 10 digits after the decimal point when the fraction $\frac17$ is written in base 16?

Answer 1

Answer:

The amswer is "2,4,9....."

Step-by-step explanation:

$x=\frac{1}{7}\\\\x_d=0.\overline{142857}\\\\x_h=0.\overline{249}$

by leave you to work out the other 7 digits:

$\to \frac{1}{7}\approx \frac{a}{16}\\\\a= \text{first hex digit}\\\\a=floor(\frac{16}{7})=2$  

$\to \frac{1}{7}- \frac{a}{16}\approx \frac{b}{16^2}\\\\b= \text{second hex digit}\\\\b=floor(\frac{16^2}{7} -16a)=4$  

$\to \frac{1}{7}- \frac{a}{16}-\frac{b}{16^2} \approx \frac{c}{16^3}\\\\c= \text{third hex digit}\\\\c=floor(\frac{16^3}{7} -16^2a-16b)=9$