In base 6, the decimal .343434..., equals what base 10 fraction?

Answer 1

Let x (base 10) = 0.343434... (base 6)
Then 36x (base 10) = 34.34343.. (base 6), since multiplying by 36 in base 6 is like multiplying by 100 in base 10.
So 35x (base 10) = 34 (base 6).
34 in base 6 is 3*6+4 = 22 in base 10.
So the answer is 22/35.

Answer 2

I hope I'm doing this correctly. The number 34 in base 6 is equivalent to (3 X 6) + (4 X 1) = 22 in base 10. Thus, the same decimal in base 10 would be .2222222..., or 2/9.

Answer 3

In base 10, the number .4321 is defined as follows:
(10^-1 * 4) + (10^-2 * 3) + (10^-3 * 2) + (10^4 * 1) =
= 0.4 + 0.03 + 0.002 + 0.0001
= 0.4321

In turn, the number 0.343434 in base 6 would be:
(6^-1 * 3) + (6^-2 * 4) + (6^-3 * 3) + (6^-4 * 4) + (6^-5 * 3) + (6^-6 * 4) =
= 0.5 + 0.11 + 0.0139 + 0.00309 + 0.000386 + 0.0000857
= 0.5174617 (approximately)

I hope, even if my answer is wrong, that this helps you figure out what "base x" means...

Answer 4

x= .343434...

100x = 34.343434.... (100 is base 6 and not 10)

so (100-1) x = 34

100-1 in base 6 = 35

23 base 6 = 17

so value = 17/35

Answer 5

stephen m dude finally got it right.

Answer 6

dont get it

Answer 7

.62857- - -