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Quantitative Reasoning – Practice – How many digits in the expression!

PSA_PRACTICE_QNR47. Find the number of digits of expression in 6^3×4^11×5^5.


Ans: 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.

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