1. The problem asks to write the decimal numbers as simplified common fractions. 2. For 11b) 0.135: - Recognize that 0.135 means 135 thousandths. - Write as fraction: $$\frac{135}{1000}$$ - Simplify by dividing numerator and denominator by 5: $$\frac{\cancel{135}^ {27}}{\cancel{1000}^{200}}$$ - Simplify further by dividing numerator and denominator by 27: $$\frac{\cancel{27}^1}{\cancel{200}^{\frac{200}{27}}}$$ - Since 200/27 is not an integer, check for common factors again: - Actually, 135 and 1000 share a factor of 5 only, so simplified fraction is $$\frac{27}{200}$$. 3. For 11c) 5.279: - Separate whole number and decimal: 5 + 0.279 - Convert 0.279 to fraction: - 0.279 = $$\frac{279}{1000}$$ - Simplify numerator and denominator by dividing by 1 (no common factors): fraction stays $$\frac{279}{1000}$$ - So, 5.279 as a mixed number is $$5 \frac{279}{1000}$$ 4. For 11d) 0.285714: - Recognize this is a repeating decimal (0.285714285714...) - This is a known repeating decimal equal to $$\frac{2}{7}$$ - Explanation: The repeating cycle 285714 corresponds to $$\frac{2}{7}$$ Final answers: - 11b) $$\frac{27}{200}$$ - 11c) $$5 \frac{279}{1000}$$ - 11d) $$\frac{2}{7}$$