Question

Determine if 0.71875 is rational or irrational and give a reason for your answer.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The number 0.71875 is a rational number.

A rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero. Let's demonstrate this for 0.71875:

If we express 0.71875 as a fraction, we can see that it is equal to 71875/100000.
Both the numerator (71875) and the denominator (100000) are integers, and the denominator is not zero. Thus, 0.71875 is a rational number.

Answer 2

The number 0.71875 is a rational number.

A. it is a decimal that repeats.
B. it is the square root of a perfect square.
C. it is a decimal that terminates.
D. it is the square root of a non-perfect square.
E. it is a decimal that does not repeat or terminate.

Answer 3

[AI-generated answer — Bot GPT 3.5]

C. it is a decimal that terminates.

0.71875 is a terminating decimal since it has a finite number of digits after the decimal point. In this case, it terminates after the two decimal places.

Answer 4

Determine if 0.68 is rational or irrational and give a reason for your answer.

A. it is a decimal that repeats.
B. it is the square root of a perfect square.
C. it is a decimal that terminates.
D. it is the square root of a non-perfect square.
E. it is a decimal that does not repeat or terminate.

Answer 5

[AI-generated answer — Bot GPT 3.5]

The number 0.68 is a rational number.

A rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero. Let's demonstrate this for 0.68:

If we express 0.68 as a fraction, it is equal to 68/100.
Both the numerator (68) and the denominator (100) are integers, and the denominator is not zero. Hence, 0.68 is a rational number.

The answer is C. It is a decimal that terminates.

Answer 6

Determine if 0, point, 5, 2, 8, 1, 7, 6, 8, 1, 7, 6, 8, 1, 7, 6, 8, 1, 7, 6, point, point, .0.528176817681768176... is rational or irrational and give a reason for your answer

A. it is a decimal that repeats.
B. it is the square root of a perfect square.
C. it is a decimal that terminates.
D. it is the square root of a non-perfect square.
E. it is a decimal that does not repeat or terminate..

Answer 7

[AI-generated answer — Bot GPT 3.5]

The number 0.528176817681768176... is a rational number.

A rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero.

Although the decimal expansion of 0.528176817681768176... continues indefinitely without any repeating pattern, it can still be written as a fraction. In this case, the decimal representation provides a pattern of repeating digits after the initial non-repeating part.

Let's express this number as a fraction:

Let x = 0.528176817681768176...
If we multiply x by 10, we get 10x = 5.28176817681768176...
Now, if we subtract x from 10x, we eliminate the non-repeating part:
10x - x = 5.28176817681768176... - 0.528176817681768176...
9x = 4.75359135913591359135...
Now, let's shift the decimal point to eliminate the non-repeating part:
1000(9x) = 4753.59135913591359135...
1000(9x - x) = 4753.59135913591359135... - 4.75359135913591359135...
999x = 4748.837767776778677865...
Simplifying further:
x = 4748.837767776778677865... / 999

The numerator (4748.837767776778677865...) and the denominator (999) are both integers, with the denominator not being zero. Therefore, 0.528176817681768176... is a rational number.

The answer is not given among the options provided.

Answer 8

Determine if 0.528176817681768176... is rational or irrational and give a reason for your answer.

A. it is a decimal that repeats.
B. it is the square root of a perfect square.
C. it is a decimal that terminates.
D. it is the square root of a non-perfect square.
E. it is a decimal that does not repeat or terminate..

Answer 9

[AI-generated answer — Bot GPT 3.5]

The number 0.528176817681768176... is rational because it is a decimal that repeats.

A rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero.

In this case, the decimal 0.528176817681768176... shows a repeating pattern of the digits 1768. This means that the decimal repeats indefinitely after a certain point.

Hence, the answer is A. It is a decimal that repeats, making it a rational number.

Answer 10

Between which two consecutive whole numbers does square root of, 17, lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of, 17,

to an approximately correct location on the number line.

Answer 11

[AI-generated answer — Bot GPT 3.5]

The square root of 17 lies between the two consecutive whole numbers 4 and 5.

To justify this answer, we need to find the whole numbers whose squares are closest to 17. The square of 4 is 16, which is less than 17, and the square of 5 is 25, which is greater than 17. Therefore, the square root of 17 falls between 4 and 5.

Please note that for a more precise placement of square root of 17 on the number line, it may be helpful to refer to a number line with marked increments.