큰 수의 지수 표현

$\displaystyle {\frac{2 ^{68} \times 5 ^{68} _{}}{{2 ^{7} \times 5 ^{7} + 2 ^{4} \times 5 ^{4}} ^{}}} = \frac{10 ^{68}}{10 ^{7} + 10 ^{4}}$ 이고 $a > 0$ 일 때, $\displaystyle y = \frac{a}{x}$ ($x > 0$)는 감소함수이므로 $\displaystyle \frac{9 \times 10 ^{68}}{10 ^{8}} < \frac{10 ^{68}}{10 ^{7} + 10 ^{4}} < \frac{10 ^{68}}{10 ^{7}}$ ($\because$$\displaystyle \frac{10 ^{8}}{9} > 10 ^{7} + 10 ^{5} > 10 ^{7}$ ) $\displaystyle \frac{9 \times 10 ^{68}}{10 ^{8}} = 9 \times 10 ^{60}$, $\displaystyle \frac{10 ^{68}}{10 ^{7}} = 10 ^{61}$ $\therefore$ $\displaystyle 9 \times 10 ^{60} < \frac{10 ^{68}}{10 ^{7} + 10 ^{4}} < 10 ^{61}$ $\therefore$ $\displaystyle \frac{10 ^{68}}{10 ^{7} + 10 ^{4}} = a \times 10 ^{60}$ ($9 < a < 10$) 이므로$n = 60$ 이다.