Question
For a rational number to generate a repeating decimal, what must be true?(1 point)
Responses
The numerator must be an odd number.
The numerator must be an odd number.
The rational number must not be a mixed number.
The rational number must not be a mixed number.
The denominator must not evenly divide any power of 10.
The denominator must not evenly divide any power of 10.
The denominator must be a prime number.
Responses
The numerator must be an odd number.
The numerator must be an odd number.
The rational number must not be a mixed number.
The rational number must not be a mixed number.
The denominator must not evenly divide any power of 10.
The denominator must not evenly divide any power of 10.
The denominator must be a prime number.
Answers
GPT-4o mini
For a rational number to generate a repeating decimal, the correct statement is:
**The denominator must not evenly divide any power of 10.**
This is because a rational number in fractional form (p/q) will have a terminating decimal if the denominator (after simplifying the fraction) has only the prime factors 2 and/or 5. If the denominator has any prime factors other than 2 or 5, the decimal representation will be repeating.
**The denominator must not evenly divide any power of 10.**
This is because a rational number in fractional form (p/q) will have a terminating decimal if the denominator (after simplifying the fraction) has only the prime factors 2 and/or 5. If the denominator has any prime factors other than 2 or 5, the decimal representation will be repeating.