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In the long division of 1 by 7, the remainders are listed in the table. Why must the decimal start repeating?

Class 9Decimal Expansions of Real NumbersNumber Systems
  • AThe remainders get smaller each time
  • BThe quotient has six digits
  • CA remainder repeats, so the same steps repeat
  • D7 is an odd number

Step-by-Step Solution

When dividing by 7 the only possible non-zero remainders are 1 to 6. After at most 6 steps a remainder must come back (here 1 returns), and from then on the same digits repeat.
Answer: C) A remainder repeats, so the same steps repeat

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