Question 980298: Find the number of digits of expression in 6^3×4^11×5^5.
Answer by onlinepsa(22)   (Show Source):
You can put this solution on YOUR website! 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
https://onlinepsa.wordpress.com
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