To determine whether the fraction [tex]\(\frac{1}{9}\)[/tex] produces a repeating decimal that starts with 0.1, let's break this down step by step.
1. Find the Decimal Representation of [tex]\(\frac{1}{9}\)[/tex]:
- When divided, [tex]\(\frac{1}{9}\)[/tex] equals approximately 0.1111...
- This decimal is clearly repeating, consisting of the digit 1 repeating indefinitely (0.1111...).
2. Evaluate the Characteristics of the Decimal:
- The fraction [tex]\(\frac{1}{9}\)[/tex] does indeed produce a repeating decimal.
- However, the repeating decimal starts immediately at 0.1 followed by further repetitions of 1.
3. Determine if it Matches the Criteria:
- The provided decimal "0.1" captures only part of the repeating sequence.
- For the decimal 0.1111..., the repeating part starts right after the decimal point, and '0.1' is the beginning of this repeating pattern.
4. Conclusion:
- The question asks if the fraction [tex]\(\frac{1}{9}\)[/tex] produces a repeating decimal that starts with 0.1.
- Since the repeating decimal of [tex]\(\frac{1}{9}\)[/tex] is indeed 0.1111..., which starts with 0.1 and continues indefinitely with 1’s.
Therefore, the correct answer is:
A. True
