QuestionIs a rational number? Choose true or false with reasons: A. True, it's an integer. B. False, it doesn't end/repeat. C. True, it has repeating digits. D. True, it's a terminating decimal.
Studdy Solution
STEP 1
Assumptions1. We understand that a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero.
. We understand that the square root of a number is a value that, when multiplied by itself, gives the original number.
3. We know that the square root of10 is not an integer.
STEP 2
We need to determine whether is a rational number. This means we need to determine whether it can be expressed as a fraction of two integers.
STEP 3
We know that the square root of10 is not an integer. This eliminates option A.
STEP 4
We know that a rational number either terminates (ends) or repeats. This eliminates option D, because the decimal representation of does not terminate.
STEP 5
We know that a rational number either terminates or repeats. This eliminates option C, because the decimal representation of does not contain repeating digits.
STEP 6
The only option left is B, which states that is not a rational number because its decimal representation never ends or repeats. This is the definition of an irrational number.
Therefore, the statement " is a rational number" is false.
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