Final answer:
The fraction that does not represent a repeating decimal among the given options is 4/5, because its denominator contains only the prime factor 5, which allows it to be expressed as a terminating decimal.
Step-by-step explanation:
The question asks which of the following fractions does not represent a repeating decimal: a) 2/3 b) 4/5 c) 9/11 d) 8/9. A repeating decimal is one where the digits after the decimal point repeat in a pattern infinitely. To determine if a fraction has a repeating decimal, it helps to consider the denominator.
For a fraction to have a non-repeating decimal, the denominator (when in simplest form) should only contain the prime factors 2, 5, or both, as these are the factors of 10, the base of our number system.
- 2/3 has a denominator of 3, which indicates a repeating decimal.
- 4/5 has a denominator of 5, which means it can be expressed as a terminating decimal.
- 9/11 has a denominator of 11, signaling a repeating decimal.
- 8/9 has a denominator of 9, also pointing towards a repeating decimal.
Therefore, the fraction that does not represent a repeating decimal is b) 4/5.