Tricimal

[ryan_kidz]

A tricimal is like a decimal, excet the digits represent fractions with powers of 3 instead of 10. FOr example, 16/27 = 1/3 + 2/9 +1/27 = 0.121 as a tricimal.
How is 77/81 expressed as a tricimal?

I got really confused with that problem. it looks not that complicated, but i still can't figure it out.

any brilliant people can help me?

 

[galactus]

Do you know how to convert bases?. Convert your numbers to from base 10 to base 3.

Let's do 77. Repeatedly divide by 3, keep track of remainders:

77/3=25 remainder 2

25/3=8, remainder 1

8/3=2, remainder 2


The base 3 representation of 77 is, from the top, equal to 2212.

81 is easy.

81/3=27, remainder 0

27/3=9, remainder 0

9/3=3, remainder 0

3/3=1, remainder 0

81=10,000

 

[ryan_kidz]

Do you know how to convert bases?. Convert your numbers to from base 10 to base 3.

Let's do 77. Repeatedly divide by 3, keep track of remainders:

77/3=25 remainder 2

25/3=8, remainder 1

8/3=2, remainder 2


The base 3 representation of 77 is, from the top, equal to 2212.

81 is easy.

81/3=27, remainder 0

27/3=9, remainder 0

9/3=3, remainder 0

3/3=1, remainder 0

81=10,000

I don't know how to convert bases

Thnx for the explaination.

 

[ryan_kidz]

Wait.. Can u explain to me how to convert bases?

I just want to know more about that.

thnx! :wink:

 

[stapel]

We really can't teach classes here. (We deal with specific questions on particular exercises.) Try doing a search, maybe on Google, for change-of-base lessons.

Eliz.

 

[soroban]

Hello, ryan_kidz!

How is \(\displaystyle \frac{77}{81}\) expressed as a tricimal?

We already have: .\(\displaystyle \L\frac{77}{3^4}\)

Express \(\displaystyle 77\) in base-3.. . \(\displaystyle \L77 \:= \:2\cdot3^3 + 2\cdot3^2 + 1\cdot3 + 2\cdot1\)

The fraction becomes: .\(\displaystyle \L\frac{2\cdot3^3\,+\,2\cdot3^2\,+\,1\cdot3\,+\,2\cdot1}{3^4}\;= \;\frac{2}{3^1} + \frac{2}{3^2} + \frac{1}{3^3} + \frac{2}{3^4}\)


Therefore: .\(\displaystyle \L\frac{77}{81} \;= \;0.2212_{_3}\)

 

[ryan_kidz]

I see!
Thnx alot dude!