What is the repeating part in the decimal (0.1252525\ldots)?
Answer and explanation
Correct answer: (25)
A recurring decimal contains a block of digits that continues to repeat in the same order indefinitely. In the decimal 0.1252525..., the first digit after the decimal point is 1. After that initial non-repeating digit, the digits are 25, 25, 25, and so on. Thus, the repeating block must be identified from the continuous repetition, not by taking every digit from the beginning.
The decimal can be viewed as 0.1 followed by the recurring sequence 25. Since 25 reappears without interruption, the recurring part is 25, which is option C. The digit 1 is only a preliminary, non-repeating digit. The choice 125 is also not correct because it does not repeat as one complete block in the displayed decimal.
Frequently asked questions
What is the correct answer to this question?
(25)
Why is this the correct answer?
A recurring decimal contains a block of digits that continues to repeat in the same order indefinitely. In the decimal 0.1252525..., the first digit after the decimal point is 1. After that initial non-repeating digit, the digits are 25, 25, 25, and so on. Thus, the repeating block must be identified from the continuous repetition, not by taking every digit from the beginning.
The decimal can be viewed as 0.1 followed by the recurring sequence 25. Since 25 reappears without interruption, the recurring part is 25, which is option C. The digit 1 is only a preliminary, non-repeating digit. The choice 125 is also not correct because it does not repeat as one complete block in the displayed decimal.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
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