base manipulation for repeating decimals?

langris5 · Senior Member

base manipulation for repeating decimals?

vvr1590 · Senior Member

It shouldn't be inappropriate... I've seen it on several dr. numsen tests...

anyway, so far the only form of repeating decimals in different bases I've seen on tests is .aaaaaaa; they'll probably stick to this for district, we can talk about other forms before regionals (If i make it)

Repeating decimals in different bases is done pretty much the same as in base 10. In base 10, you take the number (a) and stick a 9 under it, well, in different bases, say base N, you put the number (a) over N - 1.

So in your example,

.4444 base 5 = 4/(5-1) = 4/4 = 1

this is kinda the same as how .9999 equals one

- say they gave 0.33333 in base 7 equals what in base 10? the answer would be 3/(7-1) = 1/2.

hope that helps,

vinay

-- Edited by vvr1590 at 19:01, 2005-03-25

langris5 · Senior Member

thanks lots Vinay, so .66666 in base7 is 1 in base 10? got it. Hope you make it to region and then state. Good luck.

thanks

quincy

vvr1590 · Senior Member

Yeah, you're right, .666.. in base seven would be one in base 10.

Hope you make region and state too.

So let's try to find out what to do fora repeating decimal in a different form and different base, for example

.34444444 in base 6 = what in base 10?

the first step I think would be 34-3 = 31, which would be the numerator, but then what for the denominator? maybe 50, since in base 10 it would be 90?

that would give 31/50, which I don't know is right or wrong. i have a graphing program on my calculator; when I find it, i'll get back to you.

Do you have any ideas?

Thanks,

Vinay

langris5 · Senior Member

hey vinay

i just did some online research...i think you are right, or at least very very close,because the official way of doing this problem would be

3*6^-1(-1 power because it's one place behind the decimal)+4*6^-2(-2 because it's 2 place behind the decimal)+4*6^-3....and so on...

so the problem becomes

.5+.111111(repeating)+.0185185185 (repeating)....and so on, there is no way to get the "exact" answer, therefore we can conclude that the answer is about 0.6296295, and your answer, 31/50, came out to be 0.62, i think this is good enough for any ns test, however, i am not 100% sure.

hope that helped a lil

quincy

vvr1590 · Senior Member

Yeah,

but I think that if whatever site you looked at was right, they'll probably stick to the .aaaa think with only one number repeating. And doing that is no problem.

Good luck at district,

Vinay