Question 269362
How many digits are in the number {{{5^72 * 2^74}}} ?
<pre><font size = 4 color = "indigo"><b>

{{{1*10^0=1}}} through {{{9*10^0=9}}} has 1 digit.
{{{1*10^1=10}}} through {{{9*10^1=90}}} has 2 digits.
{{{1*10^2=100}}} through {{{9*10^2=900}}} has 3 digits.
{{{1*10^3=1000}}} through {{{9*10^3=9000}}} has 4 digits.
{{{1*10^4=10000}}} through {{{9*10^4=90000}}} has 5 digits.
     ...
{{{1*10^n=10000}}}{{{"...0"}}} through {{{9*10^n=9000}}}{{{"...0"}}} has n+1 digits.

So we see the pattern here that the power of 10 in any scientific
notation is one less than the number of digits.  Therefore, 

{{{5^72 * 2^74=5^72*2^(72+2)=5^72*2^72*2^2=(5*2)^72*4=4*10^72}}}

has 73 digits. 

Edwin</pre>