(1.3125)₁₀ is represented as 1.5 in which of the following base ?

To find the base where (1.3125)₁₀ equals 1.5, we analyze the fractional part. In base $b$, the representation 1.5 means $1 + \frac{5}{b}$. We set this equal to the decimal value 1.3125: $1 + \frac{5}{b} = 1.3125$. Subtracting 1 from both sides gives $\frac{5}{b} = 0.3125$. Solving for $b$, we get $b = \frac{5}{0.3125}$. Since $0.3125 = \frac{5}{16}$, the equation becomes $b = \frac{5}{5/16} = 16$. Thus, the base is 16. Option A (base 8) would yield $1 + \frac{5}{8} = 1.625$, which is incorrect. Option B (base 12) would yield $1 + \frac{5}{12} \approx 1.417$, also incorrect. Therefore, the correct base is hexadecimal (base 16).