Converting 43.3 from Base 7 to Base 8

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Discussion Overview

The discussion revolves around the conversion of the number (43.3) from base 7 to base 8, focusing on the requirement to truncate any remainder and limit the octal representation to one digit to the right of the radix point. Participants explore the conversion process and the implications of their calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant states that (43.3) in base 7 converts to (31.42857) in decimal, questioning the correctness of their answer as (37.42684) in octal.
  • Another participant corrects the first by asserting that the conversion of (43.3) base 7 to decimal is indeed (31.42857), emphasizing that the decimal part has not yet been converted to octal.
  • A third participant reiterates that the decimal part remains in decimal form and confirms that (37) is correct, while also providing a calculation for the decimal part (0.42857...).
  • Further clarification is provided regarding the calculation of the decimal part, with one participant suggesting that the expression should involve negative powers of 7, leading to a proposed answer of (37.3...).
  • Another participant questions the notation used in the calculations, suggesting that there may have been a misunderstanding regarding the representation of the decimal part.

Areas of Agreement / Disagreement

Participants express differing views on the conversion process and the representation of the decimal part, indicating that there is no consensus on the correct approach or final answer.

Contextual Notes

There are unresolved aspects regarding the conversion of the decimal portion from base 7 to octal, as well as the notation used in the calculations, which may lead to confusion.

ccky
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Homework Statement


Convert(43.3)7to base 8?using no more than one octal digit to the right of the radix point.Truncate any remainder by chopping excess digits.Use an ordinary unsigned octal representation.


Homework Equations


Base8,decimal.


The Attempt at a Solution


(43.3）7 .Than,(31.42857)8, My answer is 37.42684 non-terminating.
Is it right or not?
Thanks.
 
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'...using no more than one octal digit to the right of the radix point.'

43.3 base 7 is equal to 31.42857 decimal, not octal. Check your conversion of 0.3 base 7 to octal.
 
The part to the right of the decimal is still decimal, not yet converted to octal (and the 37 is correct)
 
phinds said:
The part to the right of the decimal is still decimal, not yet converted to octal (and the 37 is correct)
71x3 =0.42857...
The answer is 37.3...
Is it that?
 
ccky said:
71x3 =0.42857...
?
You must have meant 7-1 x 3
ccky said:
The answer is 37.3...
Is it that?
.4285710 = 4 * 10-1 + 2 * 10-2 + 8 * 10-3 + 5 * 10-4 + 7 * 10-5

Now you need to convert this into a sum of negative powers of 8.
 

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