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Q.

Write in decimal form and say what kind of decimal expansion it has:

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a

0. 230769, terminating and non-repeating

b

0. 230769, non-terminating and repeating

c

0. 230769, non-terminating and non-repeating

d

0. 230769, terminating and repeating

answer is B.

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Detailed Solution

Concept: To solve this question, run a long division. Divide 3 by 13 until no further division is possible, or until the number after the decimal point of the quotient is repeated. If the number 3 is completely divided by 13 and cannot be divided any further, it is said to be finished. If the division lasts indefinitely, it is said to never end. When a number begins to repeat, we say it repeats. If the number is decimal and does not follow a particular repeating pattern, it is said to be non-repeating.
By using long division method divide 3 by 13
Question Image

Question Image

Therefore, the number of digits after the decimal point of the quotient is repeated and never ends.
Therefore, the decimal number

is 0. 230769 and never ends and repeats.
Hence, the correct answer is option (2)

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