SOLUTION: When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
\[0.\overline{0121}
Algebra.Com
Question 1207611: When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
\[0.\overline{0121}_3 = 0.01210121 \dots,\]
which is repeating.
When $\frac{1}{288}$ is expressed in base $35,$ is it terminating or repeating?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
If in the fraction the denominator is relatively prime to the base b,
then this fraction in base b is repeating.
This general rule is ALWAYS valid.
Apply it in your case. The fraction has the denominator 288 relatively prime to the base 35.
THEREFORE, the given fraction in the given base is repeating.
Solved, answered and explained.
RELATED QUESTIONS
When fractions are expressed in different bases, they can be terminating or repeating.... (answered by greenestamps,ikleyn)
Can someone PLEASE HELP me with this problem, I really do NOT understand any of this... (answered by Edwin McCravy)
Which of the following fractions have terminating decimals and which have repeating... (answered by checkley71)
How many ways can the value 13 be expressed as the sum of exactly 3 different positive... (answered by jim_thompson5910)
Fraction Decimal Form Terminate? Prime Factorization of the denominator
1/2
1/3
(answered by CubeyThePenguin)
What would (3x^(2/5))*(2x^(1/2)) be?
I understand how to multiply fractional exponents... (answered by Alan3354)
Two numbers a and b, are randomly selected without replacement from the set... (answered by jim_thompson5910)
7. One common use of positive and negative exponents is in writing numbers as scientific... (answered by Alan3354)
One common use of positive and negative exponents is in writing numbers as scientific... (answered by stanbon)