a)The number 19 to the power 100(sexdecillion) is called a 'Googol'!If it takes 1/5 secod to write a zero and 1/10 second to write a 'one', how long would it take to write the number 100 'Googols' in full
b)The number 10 to the power of a 'Googol'is called a 'Googololplex'.Using the same speed of writing,how long in years would it take to write 1'Googoloplex' in full?You may assume that you pen has enough ink.
To answer both questions, we can calculate the time it takes to write a single zero or one, and then multiply it by the number of digits required to write the given numbers.
a) Writing the number 19 to the power of 100 'Googols' involves writing a 1 followed by 100 'Googols' zeros. To calculate the time required in seconds, we need to find the number of zeros in 100 'Googols'.
1 'Googol' is 10 to the power of 100, which means it has 100 zeros.
Thus, 100 'Googols' would have 100 * 100 zeros.
To calculate the time to write a single zero or one, we know that it takes 1/5 second to write a zero and 1/10 second to write a one.
Now, let's calculate the time required to write 100 'Googols':
Number of zeros = 100 * 100 = 10,000
Number of ones = 1
Time required to write zeros = 10,000 * (1/5) s = 2000 s
Time required to write ones = 1 * (1/10) s = 0.1 s
Total time required = Time for zeros + Time for ones = 2000 s + 0.1 s = 2000.1 seconds.
b) Writing the number 10 to the power of a 'Googololplex' involves writing a 1 followed by 'Googololplex' zeros. Let's assume that a 'Googololplex' has 10^100 zeros.
To calculate the time in years required to write 'Googololplex', we need to find the number of zeros:
Number of zeros = 'Googololplex' = 10^100
Using the same speed of writing, let's calculate the time required to write 'Googololplex':
Time required to write zeros = 'Googololplex' * (1/5) s = (10^100) * (1/5) s
Now, let's calculate the time required in years:
Number of seconds in a year = 365 days * 24 hours * 60 minutes * 60 seconds = 31,536,000 s (approximately)
Total time required in years = (10^100 * (1/5) s) / (31,536,000 s/year)
Please note that the resulting time might be an extremely large number, given the magnitude of the 'Googololplex'.