
The decimal expansion of is:
A. A whole number
B. Terminating
C. Non – terminating but repeating
D. Non – terminating but non – repeating
Answer
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Hint: First of all we will have to know about . Actually, it is the ratio of the circumference of any circle to the diameter of that circle. The value of is equal to in rational form but in decimal we cannot calculate its exact values. In decimal it is equal to 3.141592……
Complete step-by-step answer:
We have been asked to find the decimal expansion of .
Since, we know that is the ratio of the circumference of any circle to the diameter of that circle and the value of in rational form is equal to . But, on decimal form we cannot find its exact value and it is equal to 3.141592…….
So, we will check all the options one by one.
A. Whole number
but as we know whole number are counting number including zero.
Hence, this option is incorrect.
B. Terminating
We know that terminating means a decimal having finite number after the decimal point but we can’t find the value of upto finite value.
Hence, this option is incorrect.
C. Non – terminating but repeating
It is true that the decimal expansion of is non – terminating but its digits not repeating after the decimal.
Hence, this option is incorrect.
D. Non – terminating but non – repeating
It is true that the decimal expansion of is non – terminating as well as non – repeating.
Hence, this option is correct.
Therefore, the correct option is D.
Note: Also, remember that fact about that the ratio of circumference of any circle to the diameter of that circle doesn’t change regardless of the circle’s size, this ratio always equal to .
Also, while solving the questions we usually take or in decimal form it is 3.14.
Complete step-by-step answer:
We have been asked to find the decimal expansion of
Since, we know that
So, we will check all the options one by one.
A. Whole number
Hence, this option is incorrect.
B. Terminating
We know that terminating means a decimal having finite number after the decimal point but we can’t find the value of
Hence, this option is incorrect.
C. Non – terminating but repeating
It is true that the decimal expansion of
Hence, this option is incorrect.
D. Non – terminating but non – repeating
It is true that the decimal expansion of
Hence, this option is correct.
Therefore, the correct option is D.
Note: Also, remember that fact about
Also, while solving the questions we usually take
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