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I am trying to represent $(43.3)_7$ in base-8.

But in only one integer digit by truncating the rest and using the numerical unsigned representation.

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    Why in the hell would anyone bother editing a thread that this 5 years and 2 months old?????????? – 2017-12-13

4 Answers 4

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Let's look at the definition of these things.

Interpreting

$43.3_7 = 4\cdot 7^1 + 3\cdot 7^0 + 3\cdot 7^{-1} \approx 31.4286_{10}.$

Now we change to base $8$. We have $8^2 = 64$ is too large, so the first digit we look at will be $8^1$. We have $31.4286/8 \approx 3.9285$ so the first digit will be a $3$.

Assuming by "one integer digit" you mean to truncate the result here, then the answer would be $3_8$.

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I’m going to ignore the second paragraph, since it looks as if something has been omitted from it. The number in question, in elementary-school notation, is $31\frac{3}{7}$. Since the base-$8$ expansion of $1/7$ is $.1111\cdots$, in base-$8$, the number in question is $37.3333\cdots$. We leave it to OP to round.

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As best I can read the second paragraph, you want one character (digit?) in the fractional part(beyond the decimal point?). $43_7=31_{10}=37_8$ for the integer part. For the fraction $\frac 37$ is closer to $\frac 38$ than $\frac 48$, so it would be $37.3_8$ is the closest.

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$43.3_7 = 4*7 + 3 + \frac 37=$

$4(2*3 + 1) + 3 + \frac 37*\frac 88=$

$8*3 + (4+3) + \frac{\frac {24}7}8=$

$3*8 + 7 + \frac 38 + \frac 37\frac 18=$

$3*8 + 7*8^0 + 3*8^{-1} + \frac {24}7*8^{-2}=$

$3*8 + 7*8^0 + 3*8^{-1} + 3*8^{-2}+ \frac 37*8^{-2} =$

.... via induction....

$3*8 + 7*8^0 + 3*8^{-1} + 3*8^{-2} + 3*8^{-3} + ...... = $

$37.\overline 3_8$

....

It's worth noting that just like calculating in base 10.

$\frac 17 = $

$7 $ divided into $1$

or $7$ divided into $\frac 88 = \frac 18 + $ $7$ divided into $\frac 18$

or $\frac 18 + $ $7$ divided into $\frac 8{8^2} =\frac 18 + \frac 1{8^2} + $ $ 7$ divided into $ \frac 1 {8^3}$ and so on .... $=$

$\frac 18 + \frac 1{8^2} + \frac 1{8^3} + .... = $

$.111111...._7$ so

$\frac 37 = 0.\overline 3_8$.

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    GODDAMN THESE STUPID ZOMBIE THREADS!!!!!! – 2017-12-13