Convert the binary number 1011 to base 10.

March 18, 2026Mathematics

ScanSolve AI Answer

March 18, 2026

Answer

113

Step 1: A power of 10 is written as $10^{k} = 1$ followed by $k$ zeros.

For $k = 112$ , $10^{112}$ is 1 followed by 112 zeros.

Step 2: The total number of digits is the digit 1 plus the 112 zeros.

$1 + 112 = 113$

Alternatively, using the formula for the number of digits $d$ in $n > 0$ :

$d = \lfloor \log_{10} n \rfloor + 1$

Substitute $n = 10^{112}$ :

$\log_{10} (10^{112}) = 112$

$\lfloor 112 \rfloor + 1 = 112 + 1 = 113$

10^{112} has 113 digits.

$\boxed{113}$

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Quick Answer

A power of 10 is written as 10^k = 1 followed by k zeros. For k = 112, 10^112 is 1 followed by 112 zeros.

Asked on March 18, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 18, 2026

Step 1: A power of 10 is written as 10^k = 1 followed by k zeros. For k = 112, 10^112 is 1 followed by 112 zeros. Step 2: The total number of digits is the digit 1 plus the 112 zeros. 1 + 112 = 113 Alternatively, using the formula for the number of digits d in n > 0: d = _10 n + 1 Substitute n = 10^112: _10 (10^112) = 112 112 + 1 = 112 + 1 = 113 10^112 has 113 digits. 113