How Do You Convert 212 from Decimal to Base-9?

[soopo]

Homework Statement

How can you convert 212 in base-10 to base-9?

The Attempt at a Solution

There are holes in the sequence of figures when considering 212 in base-9.
There are 21 holes in the line. There also holes from 90 to 99 and from 190 to 199.
There are then 40 (= 23+10+10-1) holes in the line, since 198 belongs to the previous sets already.
This suggests me that the figure in base-9 is at least 242.
However, the correct answer is 248.

 

[Mark44]

212₁₀ = 2*10² + 1*10¹ + 2*10⁰

What you want to do is write this number as the sum of multiples of powers of 9, which are 1, 9, 81, 243, and so on.

How many 81's (= 9²) are there? That will be you digit in the 9² place.
If there's a remainder after subtracting of the 81's, how many 9's are there in that remainder? That will be your digit in the 9's place.
If there's a remainder (and it better be 5) that will be your 1's place.

If you're converting 212₁₀ to its base-9 equivalent, 248 IS NOT the correct answer. I don't understand what you're talking about with holes in the line.

 

[icystrike]

Homework Statement

How can you convert 212 in base-10 to base-9?

The Attempt at a Solution

There are holes in the sequence of figures when considering 212 in base-9.
There are 21 holes in the line. There also holes from 90 to 99 and from 190 to 199.
There are then 40 (= 23+10+10-1) holes in the line, since 198 belongs to the previous sets already.
This suggests me that the figure in base-9 is at least 242.
However, the correct answer is 248.

The answer should be $$(255)_{9}$$ . Correct me if I'm wrong.
212=207+5=23*9+5
23=2*9+5
2=0*9+2

Combining all together,

212=9(2*9+5)+5=2*9²+5*9+5
Suggesting 212=$$(255)_{9}$$

 

[ideasrule]

Yes, 255 is right. That's easy enough to check: 2*9^2+5*9+5=212.

 

[HallsofIvy]

The quick way to do this is: divide 212 by 9. 9 divides into 212 23 times with remainder 5. 9 divides into 23 twice with remainder 5: 212₁₀= 255₉.

That is because saying that 9 divides into 212 23 times with remainder 5 means that 212= 9(23)+ 5. Since 9 divides into 23 twice with remainder 5, 212= 9(9(2)+ 5)+ 5= 2(9²)+ 5(9)+ 5.