Solve 3/2-785*10^6*3,14*(1*10^-3)^2/2*100*9,8

$$\frac { 3 } { 2 } - \frac { 785 \cdot 10 ^ { 6 } \cdot 3,14 \cdot ( 1 \cdot 10 ^ { - 3 } ) ^ { 2 } } { 2 \cdot 100 \cdot 9,8 }$$

Evaluate

$$\frac{4751}{19600}\approx 0,242397959$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{3}{2}-\frac{3,14\times 157\times 10^{6}\times \left(10^{-3}\right)^{2}}{2\times 9,8\times 20}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$\frac{3}{2}-\frac{3,14\times 157\times 10^{6}\times 10^{-6}}{2\times 9,8\times 20}$$

Multiply 10^{6} and 10^{-6} to get 1.

$$\frac{3}{2}-\frac{3,14\times 157}{2\times 9,8\times 20}$$

Multiply 3,14 and 157 to get 492,98.

$$\frac{3}{2}-\frac{492,98}{2\times 9,8\times 20}$$

Multiply 2 and 9,8 to get 19,6.

$$\frac{3}{2}-\frac{492,98}{19,6\times 20}$$

Multiply 19,6 and 20 to get 392.

$$\frac{3}{2}-\frac{492,98}{392}$$

Expand \frac{492,98}{392} by multiplying both numerator and the denominator by 100.

$$\frac{3}{2}-\frac{49298}{39200}$$

Reduce the fraction \frac{49298}{39200} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}-\frac{24649}{19600}$$

Subtract \frac{24649}{19600} from \frac{3}{2} to get \frac{4751}{19600}.

$$\frac{4751}{19600}$$

Factor

$$\frac{4751}{2 ^ {4} \cdot 5 ^ {2} \cdot 7 ^ {2}} = 0.24239795918367346$$