# How do I represent the following fraction in decimal? I would like to know how do I represent the following fraction represented in base-8 in decimal form ((35)/(25))8 It seems very hard. Please somebody help me.

How do I represent the following fraction in decimal?
I would like to know how do I represent the following fraction represented in base-$8$ in decimal form:
$\left(\frac{35}{25}{\right)}_{\text{8}}$
It seems very hard. Please somebody help me.
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domwaheights0m
You can do the operation in base $8$ if you can do math there. All the below is in base $8$ even though I do not show the subscript.
$\begin{array}{rl}\frac{35}{25}& =1+\frac{10}{25}\end{array}\phantom{\rule{0ex}{0ex}}=1+\frac{1}{10}\cdot \frac{100}{25}=1+\frac{3}{10}+\frac{1}{10}\cdot \frac{1}{25}\phantom{\rule{0ex}{0ex}}=1+\frac{3}{10}+\frac{1}{100}\cdot \frac{10}{25}\phantom{\rule{0ex}{0ex}}=1.303\overline{03}$
where we recognized the repeat.
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pezgirl79u
Do just what you would normally do with a base $10$ number: divide the numerator by the denominator. First:
$\frac{{35}_{8}}{{25}_{8}}={1}_{8}+\frac{{10}_{8}}{{25}_{8}}$
Now, add a zero to the end of ${10}_{8}$ to get ${100}_{8}$. Make sure that you realize that ${100}_{8}÷{25}_{8}\ne 4$, but $3$ with a remainder of $1$. So far, we have ${1.3}_{8}+\frac{{1}_{8}}{{25}_{8}}$ Continue until you get a repeating decimal.
If you can also find some number ${n}_{8}$ such that ${25}_{8}\ast {n}_{8}={7777...7}_{8}$, then you can multiply both the numerator and the denominator by ${n}_{8}$ to get some number over a number made entirely of sevens. The numerator is your repeating decimal. For instance, ${25}_{8}\ast {3}_{8}={77}_{8}$, so your repeating decimal is ${10}_{8}\ast {3}_{8}={30}_{8}$, i.e. $1.\overline{30}$