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Find the number of Zeros - 2^222xx5^55...

Find the number of Zeros -
`2^222xx5^555`

A

222

B

555

C

777

D

333

Text Solution

AI Generated Solution

The correct Answer is:
To find the number of zeros in the expression \(2^{222} \times 5^{555}\), we need to determine how many times we can form the number 10 from the factors of 2 and 5 in the expression. Each pair of one 2 and one 5 will give us one 10, which contributes one zero. ### Step-by-Step Solution: 1. **Identify the powers of 2 and 5**: - In the expression \(2^{222} \times 5^{555}\), we have: - Power of 2 = 222 - Power of 5 = 555 2. **Determine the limiting factor**: - To form a 10, we need one 2 and one 5. The number of 10s we can form is limited by the smaller of the two powers. - Here, the power of 2 is 222 and the power of 5 is 555. 3. **Calculate the number of pairs**: - Since we can only form as many pairs as the smaller power, we take the minimum of the two: \[ \text{Number of pairs} = \min(222, 555) = 222 \] 4. **Conclusion**: - Therefore, the number of zeros at the end of the number represented by \(2^{222} \times 5^{555}\) is 222. ### Final Answer: The number of zeros in \(2^{222} \times 5^{555}\) is **222**.
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