What is the recurring part in (2.4585858\ldots)?
Answer and explanation
Correct answer: (58)
In a decimal expansion, the recurring part is the block of digits that repeats indefinitely in the same order. It is important to separate any nonrepeating digits at the beginning from the repeating block. In 2.4585858…, the digits after the decimal point begin 4, 5, 8, 5, 8, 5, 8 and so on.
The digits 45 occur only once at the start of the decimal part. After them, the two-digit block 58 repeats continuously: 58, 58, 58, … . Therefore the recurring part is 58, which is choice B. The block 858 is not the basic repeating block, because it overlaps the repeated pattern and does not represent the shortest repeating unit. The initial 45 is nonrecurring.
Frequently asked questions
What is the correct answer to this question?
(58)
Why is this the correct answer?
In a decimal expansion, the recurring part is the block of digits that repeats indefinitely in the same order. It is important to separate any nonrepeating digits at the beginning from the repeating block. In 2.4585858…, the digits after the decimal point begin 4, 5, 8, 5, 8, 5, 8 and so on.
The digits 45 occur only once at the start of the decimal part. After them, the two-digit block 58 repeats continuously: 58, 58, 58, … . Therefore the recurring part is 58, which is choice B. The block 858 is not the basic repeating block, because it overlaps the repeated pattern and does not represent the shortest repeating unit. The initial 45 is nonrecurring.
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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