How is (0.41̅25) written in ordinary decimal form?
Answer and explanation
Correct answer: 0.41252525…
The key concept is interpreting repeating-decimal bar notation correctly. In 0.41̅25, the bar is intended to cover the block 25, while the digits 41 before the bar are the non-repeating part. Therefore write 41 first after the decimal point, then repeat 25 continuously: 0.41252525… . The first digits are 4, 1, 2, 5, 2, 5, 2, 5, and so on. Thus option A is correct. Option B changes the order of the repeating block, option C inserts an extra 4 and does not preserve the stated notation, and option D incorrectly treats the repeating decimal as terminating. A bar over a block means that the entire block repeats indefinitely, not that it appears only once.
Frequently asked questions
What is the correct answer to this question?
0.41252525…
Why is this the correct answer?
The key concept is interpreting repeating-decimal bar notation correctly. In 0.41̅25, the bar is intended to cover the block 25, while the digits 41 before the bar are the non-repeating part. Therefore write 41 first after the decimal point, then repeat 25 continuously: 0.41252525… . The first digits are 4, 1, 2, 5, 2, 5, 2, 5, and so on. Thus option A is correct. Option B changes the order of the repeating block, option C inserts an extra 4 and does not preserve the stated notation, and option D incorrectly treats the repeating decimal as terminating. A bar over a block means that the entire block repeats indefinitely, not that it appears only once.
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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