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lys-0071 [83]
2 years ago
15

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

Mathematics
1 answer:
Virty [35]2 years ago
8 0

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\\\\  

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Answer:

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Step-by-step explanation:

Steps

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$\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}$

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Show Steps

$x-2<-\frac{4}{5}\quad:\quad x<\frac{6}{5}$

Show Steps

$x-2>\frac{4}{5}\quad:\quad x>\frac{14}{5}$

$\mathrm{Combine\:the\:intervals}$

$x<\frac{6}{5}\quad\mathrm{or}\quad\:x>\frac{14}{5}$

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