QuestionIdentify true statements about irrational numbers in decimal form: A. Nonterminating and repeating. B. Nonrepeating. C. Terminating.
Studdy Solution
STEP 1
Assumptions1. We understand the definition of irrational numbers. . We understand the terms "nonterminating", "repeating", and "terminating" in the context of decimal representation of numbers.
STEP 2
Let's start by defining what an irrational number is. An irrational number is a number that cannot be expressed as a ratio of two integers. In other words, it cannot be written as a fraction.
STEP 3
Now, let's consider the decimal representation of irrational numbers. By definition, irrational numbers in decimal form are nonterminating.
STEP 4
This means that the decimal representation of an irrational number goes on forever without ending. So, statement A is partially correct. However, it also states that irrational numbers are repeating, which is incorrect.
STEP 5
The decimal representation of an irrational number is not only nonterminating, but also nonrepeating. This means that there is no pattern that repeats indefinitely in the decimal representation of an irrational number.
STEP 6
Therefore, statement B is correct. Irrational numbers are nonrepeating.
STEP 7
Statement C says that irrational numbers are terminating. This is incorrect because, as we established earlier, irrational numbers in decimal form are nonterminating.
STEP 8
So, the only true statement among the given options is B. Irrational numbers are nonrepeating.
The correct answer is .
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