Concept explainers
To determine: If the statement,” A real number can be written as a repeating decimal.” is always, sometimes or never true.
Answer to Problem 45PPS
Given statement is SOMETIMES true.
Explanation of Solution
Given information: A statement, “A real number can be written as a repeating decimal.”
Concept used: A real number is a set of collection of both rational as well as irrational numbers. And a rational number is either terminating or non terminating but repeating and an irrational number is one that is always non terminating, non repeating.
Thus, every rational number is real number and every irrational number separately is also a real number.
Conclusion: Thus, by above concept, it is cleared that a real number is repeating decimal only when it is a rational number that is non-terminating but repeating i.e. only in this case. So, a real number is a repeating decimal only SOMETIMES when it represents a non-terminating but repeating rational number.
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