Base converter with fractions?
01-28-2017, 01:42 PM
Post: #10
 Jan_D Member Posts: 69 Joined: Nov 2016
RE: Base converter with fractions?
(01-26-2017 06:57 PM)Han Wrote:  Here's the math for this specific example. A general program is left as an exercise for the diligent reader.

3.142 = 3 + 0.142

Convert the whole number part into base 7. Since it is only 3, then we are done. This leaves 0.142 for conversion to $$0.d_1 d_2 d_3 \dotsm$$ where the $$d_i$$ are 0 through 6. Note that if we multiply the fractional part by 7 then we will get a value that is non-negative and strictly less than 7.
\begin{align*} 0.142 & = 0.d_1 d_2 d_3 \dotsm \\ 7\cdot 0.142 & = d_1 + 0.d_2 d_3 d_4 \dotsm\\ 0.994 & = d_1 + 0.d_2 d_3 d_4 \dotsm \\ \end{align*}
Therefore $$d_1 = 0$$. Now repeat...
\begin{align*} 0.994 & = 0. d_2 d_3 d_4 \dotsm \\ 7\cdot 0.994 & = d_2 + 0.d_3 d_4 d_5 \dotsm\\ 6.958 & = d_2 + 0.d_3 d_4 d_5 \dotsm \\ \end{align*}
Therefore $$d_2 = 6$$. Rinse and repeat (subtract the integer part and repeat for the fractional part) for as many digits as you need.

Nice and efficient math, Han!
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 Messages In This Thread Base converter with fractions? - Joe Horn - 01-15-2017, 05:53 AM RE: Base converter with fractions? - Jan_D - 01-22-2017, 03:13 PM RE: Base converter with fractions? - Joe Horn - 01-22-2017, 11:22 PM RE: Base converter with fractions? - Jan_D - 01-26-2017, 12:38 PM RE: Base converter with fractions? - Joe Horn - 01-26-2017, 05:18 PM RE: Base converter with fractions? - Han - 01-27-2017, 05:00 AM RE: Base converter with fractions? - Joe Horn - 01-28-2017, 03:25 AM RE: Base converter with fractions? - Dieter - 01-28-2017, 03:15 PM RE: Base converter with fractions? - Han - 01-26-2017, 06:57 PM RE: Base converter with fractions? - Jan_D - 01-28-2017 01:42 PM RE: Base converter with fractions? - Han - 01-27-2017, 04:37 AM RE: Base converter with fractions? - Jan_D - 02-02-2017, 05:26 PM RE: Base converter with fractions? - Jan_D - 02-03-2017, 01:51 PM RE: Base converter with fractions? - Jan_D - 02-21-2017, 05:59 PM RE: Base converter with fractions? - Han - 02-21-2017, 07:30 PM RE: Base converter with fractions? - Jan_D - 02-22-2017, 06:03 PM RE: Base converter with fractions? - Gerald H - 01-28-2017, 02:58 PM RE: Base converter with fractions? - Han - 02-03-2017, 02:31 PM RE: Base converter with fractions? - toml_12953 - 02-13-2017, 02:36 PM RE: Base converter with fractions? - Jan_D - 02-03-2017, 05:52 PM RE: Base converter with fractions? - Jan_D - 02-13-2017, 01:14 PM RE: Base converter with fractions? - Han - 02-13-2017, 01:27 PM

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