Mathematics ACT Aspire Practice Test

When does division result in a terminating decimal?

1. When the numerator is larger than the denominator

2. When the remainder is zero

3. When both numbers are odd

4. When the denominator is a prime number

The correct answer is: When the remainder is zero

A division results in a terminating decimal when the denominator, after simplifying the fraction, has only the prime factors of 2 and/or 5. This means once the fraction is in its simplest form, if any other prime factors are present in the denominator, the decimal will be non-terminating. When the remainder is zero, it indicates that the numerator is exactly divisible by the denominator, leading to a whole number result, which is in itself a terminating decimal (since it can be expressed as a finite decimal number). For example, 6 divided by 3 equals 2, which can also be expressed as 2.0, a terminating decimal. In the context of division, the other options do not guarantee a terminating decimal. The size of the numerator compared to the denominator does not influence the decimal's nature (it could still be non-terminating if the criteria regarding prime factors are not met). The fact that both numbers are odd does not relate to the resulting decimal type; a fraction with odd numbers could have a denominator that is not composed of only the prime factors of 2 and 5. Lastly, whether the denominator is prime or not isn't a determining factor either; prime numbers can have factors other than 2 or