Which set contains fractions or decimals that end or have a repeating pattern?

Which set contains fractions or decimals that end or have a repeating pattern?

• A. Irrational Numbers
• B. Rational Numbers
• C. Real Numbers
• D. Integers

Answer: (B)

When a number can be written as a ratio of two integers, it is called a rational number. If you convert such a fraction to a decimal, the decimal either terminates (ends after a finite number of digits) or repeats a pattern forever (a repeating decimal). For example, 1/2 becomes 0.5, which ends, and 1/3 becomes 0.333..., which repeats. That pattern of ending or repeating is exactly what the question is describing. In contrast, irrational numbers do not have decimals that end or repeat; their digits go on without any repeating block. Real numbers include both rational and irrational numbers, so not all real numbers have terminating or repeating decimals. Integers are a subset of rational numbers, and their decimals terminate as simple whole-number decimals, but the set described by the property—numbers that can be written as a fraction and thus have terminating or repeating decimals—fits rational numbers best.

When a number can be written as a ratio of two integers, it is called a rational number. If you convert such a fraction to a decimal, the decimal either terminates (ends after a finite number of digits) or repeats a pattern forever (a repeating decimal). For example, 1/2 becomes 0.5, which ends, and 1/3 becomes 0.333..., which repeats. That pattern of ending or repeating is exactly what the question is describing.

In contrast, irrational numbers do not have decimals that end or repeat; their digits go on without any repeating block. Real numbers include both rational and irrational numbers, so not all real numbers have terminating or repeating decimals. Integers are a subset of rational numbers, and their decimals terminate as simple whole-number decimals, but the set described by the property—numbers that can be written as a fraction and thus have terminating or repeating decimals—fits rational numbers best.