The decimal expansion of the rational number 13678/1250 will terminate after
Answers
Answer:
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The given rational number is 145871250
. Now, convert the given number into a decimal value. We know that termination of digits in decimal expansion means that after a finite number of decimal places, all succeeding place values are zero. Now, check after which decimal places, the succeeding place values are equal to zero. At last, pick the correct option.
Complete step by step answer:
According to the question, we are given a rational number and we have to find the decimal place after which the decimal expansion will terminate.
The given rational number = 145871250
……………………………………(1)
We know that a rational number is in the form of pq
where q≠0
.
We can observe that the given number is also in the form of pq
and q≠0
so, no doubt the given number is rational.
Now, let us calculate the decimal value of the given number.
On converting the given rational number into decimal form, we get
1250⎞⎠⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟145871250208¯¯¯¯¯¯¯¯¯¯7125083707500870¯¯¯¯¯¯¯¯¯¯075001200011250750075000000¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯11.6696
……………………………….(2)
We know that termination of digits in decimal expansion means that after a finite number of decimal places, all succeeding place values are zero.
Answer:
Hence, given rational number will terminate after 4 decimal places
.
.
.