What is the repeating part in the decimal 1.232323...?
Answer and explanation
Correct answer: 23
The governing concept is recurring decimal notation. In 1.232323..., the digits after the decimal point are 2, 3, 2, 3, 2, 3, and so on. The two-digit block 23 repeats continuously, so the recurring part is 23 and option B is correct. The initial digit 1 is the whole-number part, not a repeating decimal block. Although the sequence also contains 32 if read from the second digit onward, 32 is not aligned with the repeated cycle beginning immediately after the decimal point; writing the decimal as 1.232323... clearly shows the period 23. The block 123 is not repeated at all. Identifying the smallest block that reproduces the decimal indefinitely is the standard way to determine the repetend.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
The governing concept is recurring decimal notation. In 1.232323..., the digits after the decimal point are 2, 3, 2, 3, 2, 3, and so on. The two-digit block 23 repeats continuously, so the recurring part is 23 and option B is correct. The initial digit 1 is the whole-number part, not a repeating decimal block. Although the sequence also contains 32 if read from the second digit onward, 32 is not aligned with the repeated cycle beginning immediately after the decimal point; writing the decimal as 1.232323... clearly shows the period 23. The block 123 is not repeated at all. Identifying the smallest block that reproduces the decimal indefinitely is the standard way to determine the repetend.
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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