Convert from base 10 to base 5

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I understand the integer part, keep dividing by 5 and I get 112, but for the fraction part I need a help.

The number is:

$$ (32.\bar 5)_{10} = (112, ??)_{5} $$ $$ 0,5 * 5 = 2,5\\ 0,5 * 5 = 2,5\\ 0,5 * 5 = 2,5\\ 0,5 * 5 = 2,5\\ $$ It's correct? $$ (32.\bar 5)_{10} = (112,\bar2)_{5} ? $$

Thanks.

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1 Answer

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Yes, this seems sensible. Recurring decimals (or quinaries?) are not a feature of the base. Compare this number in ternary, which is 1012.12 exactly. Can you convert to nonary (base 9)?

See e.g.

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