Solve [{(8.0001)^2div(1.001)^2}*9.1]div2=?

$$[ \{ ( 8.0001 ) ^ { 2 } \div ( 1.001 ) ^ { 2 } \} \times 9.1 ] \div 2 = ?$$

Evaluate

$$\frac{6400160001}{22022000}\approx 290.625737944$$

Solution Steps

Calculate 8.0001 to the power of 2 and get 64.00160001.

$$\frac{\frac{64.00160001}{1.001^{2}}\times 9.1}{2}$$

Calculate 1.001 to the power of 2 and get 1.002001.

$$\frac{\frac{64.00160001}{1.002001}\times 9.1}{2}$$

Expand \frac{64.00160001}{1.002001} by multiplying both numerator and the denominator by 100000000.

$$\frac{\frac{6400160001}{100200100}\times 9.1}{2}$$

Convert decimal number 9.1 to fraction \frac{91}{10}.

$$\frac{\frac{6400160001}{100200100}\times \frac{91}{10}}{2}$$

Multiply \frac{6400160001}{100200100} times \frac{91}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{6400160001\times 91}{100200100\times 10}}{2}$$

Do the multiplications in the fraction \frac{6400160001\times 91}{100200100\times 10}.

$$\frac{\frac{582414560091}{1002001000}}{2}$$

Reduce the fraction \frac{582414560091}{1002001000} to lowest terms by extracting and canceling out 91.

$$\frac{\frac{6400160001}{11011000}}{2}$$

Express \frac{\frac{6400160001}{11011000}}{2} as a single fraction.

$$\frac{6400160001}{11011000\times 2}$$

Multiply 11011000 and 2 to get 22022000.

$$\frac{6400160001}{22022000}$$

Factor

$$\frac{3 ^ {6} \cdot 2963 ^ {2}}{7 \cdot 13 \cdot 2 ^ {4} \cdot 5 ^ {3} \cdot 11 ^ {2}} = 290\frac{13780001}{22022000} = 290.6257379438743$$