(9 × 16²) + (10 × 16¹) + (11 × 16⁰) + (15 × 16⁻¹) + (2 × 16⁻²) + (0 × 16⁻³)

asked by guest
on Jan 15, 2025 at 1:35 am



You asked:

Evaluate the expression: \(9 \cdot {16}^{2} + 10 \cdot {16}^{1} + 11 \cdot {16}^{0} + 15 \cdot {16}^{-1} + 2 \cdot {16}^{-2} + 0 \cdot {16}^{-3}\)

MathBot Answer:

\[9 \cdot {16}^{2} + 10 \cdot {16}^{1} + 11 \cdot {16}^{0} + 15 \cdot {16}^{-1} + 2 \cdot {16}^{-2} + 0 \cdot {16}^{-3} = \frac{316921}{128} = 2475.9453125\]

\[\begin{aligned}9 \cdot {16}^{2} + 10 \cdot {16}^{1} + 11 \cdot {16}^{0} + 15 \cdot {16}^{-1} + 2 \cdot {16}^{-2} + 0 \cdot {16}^{-3}& = 9 \cdot 16^{2} + 10 \cdot 16^{1} + 11 \cdot 16^{0} + \frac{15}{16} + 2 \cdot \frac{1}{16^{2}} + 0 \cdot \frac{1}{16^{3}}\\& = 9 \cdot 256 + 10 \cdot 16^{1} + 11 \cdot 16^{0} + \frac{15}{16} + 2 \cdot \frac{1}{16^{2}} + 0 \cdot \frac{1}{16^{3}}\\& = 2304 + 10 \cdot 16^{1} + 11 \cdot 16^{0} + \frac{15}{16} + 2 \cdot \frac{1}{16^{2}} + 0 \cdot \frac{1}{16^{3}}\\& = 2304 + 10 \cdot 16 + 11 \cdot 16^{0} + \frac{15}{16} + 2 \cdot \frac{1}{16^{2}} + 0 \cdot \frac{1}{16^{3}}\\& = 2304 + 160 + 11 \cdot 16^{0} + \frac{15}{16} + 2 \cdot \frac{1}{16^{2}} + 0 \cdot \frac{1}{16^{3}}\\& = 2304 + 160 + 11 \cdot 1 + \frac{15}{16} + 2 \cdot \frac{1}{16^{2}} + 0 \cdot \frac{1}{16^{3}}\\& = 2304 + 160 + 11 + \frac{15}{16} + 2 \cdot \frac{1}{16^{2}} + 0 \cdot \frac{1}{16^{3}}\\& = 2304 + 160 + 11 + \frac{15}{16} + \frac{2}{256} + 0 \cdot \frac{1}{16^{3}}\\& = 2304 + 160 + 11 + \frac{15}{16} + \frac{1}{128} + 0 \cdot \frac{1}{16^{3}}\\& = 2304 + 160 + 11 + \frac{15}{16} + \frac{1}{128} + \frac{0}{4096}\\& = 2304 + 160 + 11 + \frac{15}{16} + \frac{1}{128} + 0\\& = 2464 + 11 + \frac{15}{16} + \frac{1}{128} + 0\\& = 2475 + \frac{15}{16} + \frac{1}{128} + 0\\& = \frac{39615}{16} + \frac{1}{128} + 0\\& = \frac{316921}{128} + 0\\& = \frac{316921}{128}\end{aligned}\]

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