Which list shows fractions that always result in a terminating decimal for values of n > 0?
The list of fractions that always result in a terminating decimal for values of n > 0 is:
1/2
1/4
1/5
1/8
1/10
1/16
1/20
1/25
1/32
1/40
These fractions have denominators that are powers of 2 or 5, which are the prime factors of 10, the base of our decimal system. When the denominator has no other prime factors, the fraction will always result in a terminating decimal.
To determine which fractions always result in a terminating decimal for values of n > 0, we need to consider their denominators. Fractions that have denominators consisting solely of factors of 2 and 5 will always yield a terminating decimal.
Here is a list of fractions with such denominators:
1/2, 1/4, 1/5, 1/8, 1/10, 1/16, 1/20, 1/25, 1/32, 1/40, 1/50, ...
The denominators in this list only include factors of 2 and 5, which are the prime factors of 10, the base of our decimal system. As a result, when these fractions are expressed as decimal numbers, they will always terminate.
For example, let's consider 1/4. When we divide 1 by 4 using long division, we get 0.25, which terminates after the hundredths place.
Similarly, 1/20 equals 0.05, and 1/25 equals 0.04. In both cases, the decimal representation terminates.
So, any fraction with a denominator consisting of only factors of 2 and 5 will always result in a terminating decimal when n > 0.