Decimals that terminate or repeat are classified as which kind of numbers?

Decimals that terminate or repeat are classified as which kind of numbers?

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

Answer: (A)

Decimals that stop or go on with a repeating block come from rational numbers. A rational number can be written as a fraction a/b where a and b are integers and b is not zero. If a decimal terminates, like 0.75, that’s just 75/100, which reduces to 3/4. If it repeats, like 0.333…, that repeating pattern equals a fraction (0.333… = 1/3). So every terminating or repeating decimal represents a ratio of integers, i.e., a rational number. Numbers that don’t terminate or repeat, such as sqrt(2) or pi, are irrational. Real numbers include both rational and irrational, and integers are themselves rational since they are a/1 for some integer a.

Decimals that stop or go on with a repeating block come from rational numbers. A rational number can be written as a fraction a/b where a and b are integers and b is not zero. If a decimal terminates, like 0.75, that’s just 75/100, which reduces to 3/4. If it repeats, like 0.333…, that repeating pattern equals a fraction (0.333… = 1/3). So every terminating or repeating decimal represents a ratio of integers, i.e., a rational number. Numbers that don’t terminate or repeat, such as sqrt(2) or pi, are irrational. Real numbers include both rational and irrational, and integers are themselves rational since they are a/1 for some integer a.