Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am trying to represent (43.3) base-7 to base-8

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

share|improve this question
    
What do you mean by your second paragraph? –  Dan Sep 23 '12 at 3:04

3 Answers 3

up vote 1 down vote accepted

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 $3_8$.

share|improve this answer

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.

share|improve this answer

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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.