
The number to the power is called a ‘Googol’. If it take second to write a zero and second to write a ‘one’ how long would it take to write the number ’Googol’ in full?
b) The number to the power of a ‘Googol’ is called a ‘Googolplex’. Using the same speed of writing, how long in years would it take to write ‘Googolplex’ in full?
Answer
498.9k+ views
Hint: For this we problem we first see calculate how many zero’s and one comes in expansion of and using time given to write one ‘one’ and one ‘zero’ we find total time to write one Googol and then by unitary method we find total time to write Googol.
Complete step-by-step answer:
For first problem, it is given one Googol =
As, we knows that for
Hence, using same fact we can say there for there are zero’s in the expansion of .
Time taken to write a ‘one ’zero’ = second
Time taken to write a ‘one’ = second
As, there is only one and in one Googol. As it is given, one Googol is .
Therefore, time taken to write one Googol is given as:
Therefore, time taken to write on Googol is seconds.
To calculate time taken to write Googol we will multiply time taken to write one Googol by .
Hence, time required to write Googol is .
Also, it is given that a Googolplex is = .
So, from above we see that in Googol and Googolplex there is a difference of zero’s present in both. Here both have one only once but the number of zeros in Googolplex are more than of Googol.
As, speed is given same so time taken to write one Googolplex time can be calculated as:
seconds.
Also, we know that there are
So, time to write one Googolplex in full in year =
Which is approximately equal to years.
Note: One year is
So year = .
Complete step-by-step answer:
For first problem, it is given one Googol =
As, we knows that for
Hence, using same fact we can say there for
Time taken to write a ‘one ’zero’ =
Time taken to write a ‘one’ =
As, there is only one
Therefore, time taken to write one Googol is given as:
Therefore, time taken to write on Googol is
To calculate time taken to write
Hence, time required to write
Also, it is given that a Googolplex is =
So, from above we see that in Googol and Googolplex there is a difference of zero’s present in both. Here both have one only once but the number of zeros in Googolplex are more than of Googol.
As, speed is given same so time taken to write one Googolplex time can be calculated as:
Also, we know that there are
So, time to write one Googolplex in full in year =
Which is approximately equal to
Note: One year is
So
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