Question:medium
What is the \(10\)'s complement of \((47)_{10}\)?
What is the \(10\)'s complement of \((47)_{10}\)?
Show Hint
10's complement of an n-digit number N is \(10^n-N\).
Updated On: Jul 20, 2026
- 52
- 53
- 54
- 55
Show Solution
The Correct Option is B
Solution and Explanation
Step 1: Recall the link between the 9's and 10's complement.
For any decimal number, the $10$'s complement is just the $9$'s complement plus $1$.
Step 2: Find the 9's complement of 47 digit by digit.
Subtract each digit of $47$ from $9$: the tens digit gives $9-4=5$ and the units digit gives $9-7=2$, so the $9$'s complement is $52$.
Step 3: Add 1 to get the 10's complement.
\[ 52+1=53 \]
Step 4: Conclude.
\[ \boxed{53} \] This matches the direct subtraction $100-47$.
For any decimal number, the $10$'s complement is just the $9$'s complement plus $1$.
Step 2: Find the 9's complement of 47 digit by digit.
Subtract each digit of $47$ from $9$: the tens digit gives $9-4=5$ and the units digit gives $9-7=2$, so the $9$'s complement is $52$.
Step 3: Add 1 to get the 10's complement.
\[ 52+1=53 \]
Step 4: Conclude.
\[ \boxed{53} \] This matches the direct subtraction $100-47$.
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