- #1
Cicnar
- 14
- 0
Why some repeating decimals have nonrepeating part? I think its blasphemy! :D Help!
Question
Example: Fraction 1/6 has a decimal notation of 0.1(6)
Why do other primes in denominator, aside from 2 and 5, cause a
nonrepeating part (numeral 1 in 0.1(6)) in decimal notation?
Difficulty
Ok, so my book says that if the denominator of a fraction contains,
aside from primes 2 and 5, some other primes like 3, 7 or others, than
only after first few nonrepeating numerals comes the repeating part,
called period.
Thoughts
I have this in my mind: 1/6=(1/2)x(1/3),
so, because 1/3 is 0.3333...,
we have 1/6=(1/2)x 0.3333...,
by distribution 1/6=(1/2)x(3/10)+(1/2)x(3/100)+(1/2)x(3/1000)+...
and now i can't see why it gives that nonrepeating part...
Question
Example: Fraction 1/6 has a decimal notation of 0.1(6)
Why do other primes in denominator, aside from 2 and 5, cause a
nonrepeating part (numeral 1 in 0.1(6)) in decimal notation?
Difficulty
Ok, so my book says that if the denominator of a fraction contains,
aside from primes 2 and 5, some other primes like 3, 7 or others, than
only after first few nonrepeating numerals comes the repeating part,
called period.
Thoughts
I have this in my mind: 1/6=(1/2)x(1/3),
so, because 1/3 is 0.3333...,
we have 1/6=(1/2)x 0.3333...,
by distribution 1/6=(1/2)x(3/10)+(1/2)x(3/100)+(1/2)x(3/1000)+...
and now i can't see why it gives that nonrepeating part...