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28 Nov 2023, 14:17
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (00:55) correct
24%
(00:48)
wrong
based on 234
sessions
History
Date
Time
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How many digits does \(100^{200}\) have?
A. 101
B. 201
C. 203
D. 400
E. 401
M40-09
A. 101
B. 201
C. 203
D. 400
E. 401
M40-09
28 Nov 2023, 20:12
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Bunuel
\(100^{200}\)
\((10^2)^{200}\)
\((10)^{400}\)
To find the number of digits, let's try to establish a pattern -
\(10^1 = 10\) ⇒ 2 digits
\(10^2 = 100\) ⇒ 3 digits
\(10^3 = 1000\) ⇒ 4 digits
.
.
\(10^n \) ⇒ n+1 digits
Hence \((10)^{400}\) has 401 digits.
Option E
06 Dec 2023, 14:15
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Bunuel
\(100^{200} = (10^2)^{200}= 10^{2*200}= 10^{400}\).
Therefore, this number consists of a 1 followed by 400 zeros, amounting to a total of 401 digits.
Answer: E.
