Question 980298
Find the number of digits of expression in 6^3×4^11×5^5.

6^3 × 4^11 × 5^5


=2^3 x 3^3 × 2^22 ×5^5.


= 2^25 x 3^3 x 5^5


= 2^20 x 3^3 x (5^5 x 2^25)


= 2^20 x 3^3 x  [100,000]


= 2^20 x 27 x  [100,000]


= (2^10)^2 x 27 x  [100,000]


= (1024)^2 x 27 x  [100,000]



To find the number of digits of 1024^2, we can take a lower value below 1024 and a higher one to see what the behaviour is:


(1000)^2 = 1000*1000 = 1,000,000 [7 digits]

(2000)^2 = 2000*2000 = 4,000,000 [7 digits]

In any case the number of digits remain same.

To, find the number of digits we can take 1000 in place of 1024;


(1024)^2 x 27 x  [100,000]

= (1000)^2 x 27 x  [100,000]

=2,700,000,000,000


Number of digits = 13.


Thanks,
PRD
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