Question:
Find the sum of the digits of \( 100^{100} - 10 \).
Find the sum of the digits of \( 100^{100} - 10 \).
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For large powers of 10, subtracting a small number like 10 can be used to quickly find the sum of digits.
Updated On: Nov 4, 2025
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Solution and Explanation
Step 1: Simplifying the number.
We need to find the sum of the digits of \( 100^{100} - 10 \). The number \( 100^{100} \) is a 1 followed by 200 zeros. Subtracting 10 from this gives: \[ 100^{100} - 10 = 999\ldots990 \] This number consists of 199 nines followed by one zero.
Step 2: Conclusion.
The sum of the digits is \( 9 \times 199 + 0 = 9 \). Hence, the correct answer is \(\boxed{9}\).
We need to find the sum of the digits of \( 100^{100} - 10 \). The number \( 100^{100} \) is a 1 followed by 200 zeros. Subtracting 10 from this gives: \[ 100^{100} - 10 = 999\ldots990 \] This number consists of 199 nines followed by one zero.
Step 2: Conclusion.
The sum of the digits is \( 9 \times 199 + 0 = 9 \). Hence, the correct answer is \(\boxed{9}\).
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