Converting 243 to Base 3 Using the Digit 5 | Number Systems Homework

[gEOdude]

Homework Statement

243 is a decimal number. You must convert it to base n, where n will be computed using the
digit (d) 5.
For example if your digit (d) was "7" , then n is
calculated as :n = d % 6 + 2 (where d = 7) = 7%6 + 2 = 3

Homework Equations

None.

The Attempt at a Solution

n = d % 6 + 2 (where d=5) = 5%6 + 2 = 3

243 to the base of 3 =
100000₃

 

[mfb]

d is given? Or does it come from somewhere else?
You used the example of d=7, I'm not sure if that was the idea of the homework problem.

 

[gEOdude]

d is given? Or does it come from somewhere else?
You used the example of d=7, I'm not sure if that was the idea of the homework problem.

d is given as 5. But when i plug it into the formula to calculate n i keep getting 3. I am probably wrong because I am not calculating it right. I am not having any difficulty with anything else, just that bit. So if i can get some assistance on calculating n with d=5 then I will be fine. Thanks.

 

[SteamKing]

d is given as 5. But when i plug it into the formula to calculate n i keep getting 3. I am probably wrong because I am not calculating it right. I am not having any difficulty with anything else, just that bit. So if i can get some assistance on calculating n with d=5 then I will be fine. Thanks.

All I know is 243₁₀ = 3⁵

Using place-value, 100000₃ = 1×3⁵ + 0×3⁴ + 0×3³ + 0×3² + 0×3¹ + 0×3⁰

 

[gEOdude]

DId i calculate n right? CAN SOMEONE TELL ME IF I CALCULATED N RIGHT OR IF IM DOING SOMETHING WRONG. PLEASE!

 

[SteamKing]

DId i calculate n right?

Beats me. I don't understand the question or the formula you posted. Can you provide a reference or other information?

 

[mfb]

Homework Statement

243 is a decimal number. You must convert it to base n, where n will be computed using the
digit (d) 5.
For example if your digit (d) was "7" , then n is
calculated as :n = d % 6 + 2 (where d = 7) = 7%6 + 2 = 3

If this is the full and exact problem statement, it is very odd.

If you plug d=5 into the formula then n won't be 3.

 

[Merlin3189]

This is indeed very strange.
You seem to have two distinct questions:
- convert a number into a different base, base n. This is very simple, so I don't think you have a problem here.
- find out what number n is. That is difficult because no one has defined n for you, just given an example using numbers conjured out of thin air!

The statement of the problem is odd to me: if n is to be computed from 5, why say (d)? And in your example, it is computed from 7, 6 and 2. If this really means (d), 6 and 2, why is 7 given a name (d) and 6 and 2 are not given names?

DId i calculate n right? CAN SOMEONE TELL ME IF I CALCULATED N RIGHT OR IF IM DOING SOMETHING WRONG. PLEASE!

So I can't tell you if you used the right formula. Using the formula you gave as an example,

:n = d % 6 + 2

and assuming % means modulo and : means nothing, then
5 % 6 + 2 <> 3 so your calculation is in error.
if % means integer division and : means nothing, then
5 % 6 + 2 <> 3 so your calculation is in error.

I can't tell which of these is the correct error, since 7 mod 6 = 1 and int( 7/6) =1 so your % could be either, but this is where your calculation seems to err, unless you can suggest another meaning for the % symbol or the : symbol.