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The number 10 to the power 100 is called a ‘Googol’. If it take 15 second to write a zero and 110 second to write a ‘one’ how long would it take to write the number 100 ’Googol’ in full?
b) The number 10 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 1 ‘Googolplex’ in full?

Answer
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Hint: For this we problem we first see calculate how many zero’s and one comes in expansion of (10)100 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 100 Googol.

Complete step-by-step answer:
For first problem, it is given one Googol = (10)100
As, we knows that for (10)2therearetwozeros,andfor(10)3therearethree.
Hence, using same fact we can say there for (10)100 there are 100 zero’s in the expansion of (10)100 .
Time taken to write a ‘one ’zero’ = 15 second
Time taken to write a ‘one’ = 110 second
As, there is only one 1 and 100 in one Googol. As it is given, one Googol is (10)100 .
Therefore, time taken to write one Googol is given as:
 110×(1)+15×(100)110+20=20110
Therefore, time taken to write on Googol is 20110 seconds.
To calculate time taken to write 100 Googol we will multiply time taken to write one Googol by 100 .
100×(20110)100×2011010×201=2010
Hence, time required to write 100 Googol is 2010seconds .
Also, it is given that a Googolplex is = (10)Googol .
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:
 110+(10)1005 seconds.
Also, we know that there are 3153600secondsinayear.
So, time to write one Googolplex in full in year = 110+(10)10053153600
Which is approximately equal to (10)93 years.

Note: One year is 365days,onedayis24hours,onehouris60minutesandoneminute,is60seconds.
So 1 year = 365×24×60×60=31536000seconds .
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