Final answer:
To convert the fraction 47/67 into a decimal, divide 47 by 67. The result is a non-terminating repeating decimal because the denominator 67 is a prime which does not include the factors 2 or 5.
Step-by-step explanation:
To change the fraction 47/67 into a decimal, you must divide 47 by 67. Doing this calculation with a calculator or by long division, you should get a result that starts with 0.7014... Since the division does not terminate or result in a repeating pattern immediately, we need to explore it further to determine if it's terminating or non-terminating or repeating.
A fraction will have a terminating decimal expansion if the denominator (after simplifying the fraction) has no prime factors other than 2 or 5. Since the prime factorization of 67 is just 67 (because it's a prime number and doesn't include 2 or 5), the decimal expansion of 47/67 cannot be terminating. Therefore, it will either be non-terminating repeating or non-terminating non-repeating. As 67 is a prime number, the fraction 47/67 will have a non-terminating repeating decimal.