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Mymensingh higher secondary 2019#1

Posted: Sat Feb 23, 2019 1:20 pm
by samiul_samin
How many digits in the following number?

$2^{2017}\times 7^3\times 5^{2018}$

Re: Mymensingh higher secondary 2019#1

Posted: Sun Mar 10, 2019 4:06 pm
by samiul_samin
Answer
$\fbox {2021}$

$Sol^n$
\[2^{2017}\times 5^{2018}\times7^3\]
\[=10^{2017}\times 5\times 343\]
\[=10^{2017}\times 1715\]
\[=1715\underbrace{000\cdots 0}_{2017}\]

So total digit$=2017+4=\fbox {2021}$

Re: Mymensingh higher secondary 2019#1

Posted: Sun Mar 10, 2019 4:20 pm
by vyper47
Shouldn't it be $5^{2018}$ instead of $5^{2017}$?

Re: Mymensingh higher secondary 2019#1

Posted: Sun Mar 10, 2019 4:25 pm
by samiul_samin
vyper47 wrote:
Sun Mar 10, 2019 4:20 pm
Shouldn't it be $5^{2018}$ instead of $5^{2017}$?
Yes.