1/9 and 8/9 are represented in decimal form as which of the following?

• A. 0.11 and 0.88
• B. 0.11 repeating, 0.22 repeating, and so on
• C. 0.111 repeating and 0.888 repeating
• D. 0.111 and 0.222

Answer: (B)

Think in terms of repeating decimals. When you divide by 9, you get a decimal that goes on forever without ending. Specifically, 1/9 = 0.111111... and 8/9 = 0.888888.... You can view these as repeating blocks: 0.\overline{11} equals 0.111111... and 0.\overline{88} equals 0.888888... This matches the pattern described by saying 0.11 repeating, 0.22 repeating, and so on, since the nine’s fractions produce repeating sequences where the same digits repeat indefinitely (11, 22, 33, ..., 88). The phrase “and so on” signals that same-kind repeating blocks continue for the other ninths as well.

Finite decimals like 0.11 or 0.222 are not exact representations of these fractions, so they’re not correct. And while writing 0.111 repeating or 0.888 repeating is another valid way to express the same idea, the option that clearly shows the consistent repeating pattern across the ninths is the best match.