Find number of digits

How many digits are in 2 5 × 5 6 × 1 0 9 2^{5}×5^{6}×10^{9} ?


The answer is 15.

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2 solutions

Farhabi Mojib
Apr 30, 2014

Here 2 5 2^5 × \times 5 6 5^6 × \times 1 0 9 = 2 5 10^9 = 2^5 × \times 5 5 × 1 0 9 × 5 5^5 \times 10^9 \times 5
= ( 2 × 5 ) 5 × 1 0 9 × 5 =(2\times5)^5 \times 10^9 \times 5 = 1 0 5 × 1 0 9 × 5 =10^5 \times 10^9 \times 5 = 1 0 14 × 5 =10^{14} \times 5
Clearly there are 15 15 digits in 1 0 14 × 5 10^{14} \times 5 .

Azeem King
Apr 30, 2014

2^5x5^6= 6 digits......... So, that six digit multiplied by 10^9(which have 9 digit) gives 15 digits............

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