Solve 49!+48/50!

$$\frac{ 49 ! +48 }{ 50 ! }$$

Evaluate

$$\frac{12672538834047240851505253402526987018490683987066880000000001}{633626941702362042575262670126349350924534199353344000000000000}\approx 0.02$$

Solution Steps

The factorial of 49 is 608281864034267560872252163321295376887552831379210240000000000.

$$\frac{608281864034267560872252163321295376887552831379210240000000000+48}{50!}$$

Add 608281864034267560872252163321295376887552831379210240000000000 and 48 to get 608281864034267560872252163321295376887552831379210240000000048.

$$\frac{608281864034267560872252163321295376887552831379210240000000048}{50!}$$

The factorial of 50 is 30414093201713378043612608166064768844377641568960512000000000000.

$$\frac{608281864034267560872252163321295376887552831379210240000000048}{30414093201713378043612608166064768844377641568960512000000000000}$$

Reduce the fraction \frac{608281864034267560872252163321295376887552831379210240000000048}{30414093201713378043612608166064768844377641568960512000000000000} to lowest terms by extracting and canceling out 48.

$$\frac{12672538834047240851505253402526987018490683987066880000000001}{633626941702362042575262670126349350924534199353344000000000000}$$

Factor

$$\frac{61 \cdot 271 \cdot 1459 \cdot 2731 \cdot 7013 \cdot 27433655076195791694394804758998347954292244623}{2 ^ {43} \cdot 3 ^ {21} \cdot 5 ^ {12} \cdot 7 ^ {8} \cdot 11 ^ {4} \cdot 13 ^ {3} \cdot 17 ^ {2} \cdot 19 ^ {2} \cdot 23 ^ {2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47} = 0.019999999999999997$$