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Convert \( 101.011_{\text {two }} \) to base ten

Ask by Knight Romero. in Nigeria
Mar 15,2025

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\(101.011_{\text{two}}\) is equal to \(5.375\) in base ten.

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To convert the binary number \( 101.011_{\text{two}} \) to base ten, we can break it down into its integer and fractional parts. The integer part is \( 101_{\text{two}} \): \[ 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5 \] The fractional part is \( 0.011_{\text{two}} \): \[ 0 \times 2^{-1} + 1 \times 2^{-2} + 1 \times 2^{-3} = 0 + \frac{1}{4} + \frac{1}{8} = 0.25 + 0.125 = 0.375 \] Combining both parts, we get: \[ 5 + 0.375 = 5.375 \] Thus, \( 101.011_{\text{two}} = 5.375_{\text{ten}} \).

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