1. **Stating the problem:** We need to predict if the decimal form of each given fraction is terminating or non-terminating (repeating). 2. **Recall:** A fraction \( \frac{a}{b} \) in simplest form has a terminating decimal if and only if the prime factorization of the denominator \( b \) contains only 2's and/or 5's. 3. **Analyze each fraction:** a) \( \frac{3}{8} \): Denominator 8 factors as \( 2^3 \). Only 2's, so decimal is terminating. b) \( \frac{7}{12} \): Denominator 12 factors as \( 2^2 \times 3 \). Contains 3, so decimal is non-terminating repeating. c) \( \frac{5}{6} \): Denominator 6 factors as \( 2 \times 3 \). Contains 3, so decimal is non-terminating repeating. d) \( \frac{4}{25} \): Denominator 25 factors as \( 5^2 \). Only 5's, so decimal is terminating. e) \( \frac{2}{9} \): Denominator 9 factors as \( 3^2 \). Contains 3, so decimal is non-terminating repeating. f) \( \frac{11}{40} \): Denominator 40 factors as \( 2^3 \times 5 \). Only 2's and 5's, so decimal is terminating. 4. **Final answers:** - a) Terminating - b) Non-terminating (repeating) - c) Non-terminating (repeating) - d) Terminating - e) Non-terminating (repeating) - f) Terminating