Power of 3

The formula for counting 3s is expressed as

$\sum _{ i=1 }^{ k }{ \left\lfloor \frac { 100 }{ { 3 }^{ i } } \right\rfloor }$

we normally stop when the floor function returns zero.

$\left\lfloor \frac { 100 }{ 3 } \right\rfloor +\left\lfloor \frac { 100 }{ 9 } \right\rfloor +\left\lfloor \frac { 100 }{ 27 } \right\rfloor +\left\lfloor \frac { 100 }{ 81 } \right\rfloor$

Anything ahead of 81 will return 0. Hence the sum is 48.