Solve 3.79/1(0.0955+1.5*50^2/21.15*2152*9.8)-0.069

$$\frac { 3.79 } { 1 } ( 0.0955 + \frac { 1.5 \times 50 ^ { 2 } } { 21.15 \times 2152 \times 9.8 } ) - 0.069$$

Evaluate

$$\frac{120732636869}{371704200000}\approx 0.324808374$$

Solution Steps

Anything divided by one gives itself.

$$3.79\left(0.0955+\frac{1.5\times 50^{2}}{21.15\times 2152\times 9.8}\right)-0.069$$

Calculate 50 to the power of 2 and get 2500.

$$3.79\left(0.0955+\frac{1.5\times 2500}{21.15\times 2152\times 9.8}\right)-0.069$$

Multiply 1.5 and 2500 to get 3750.

$$3.79\left(0.0955+\frac{3750}{21.15\times 2152\times 9.8}\right)-0.069$$

Multiply 21.15 and 2152 to get 45514.8.

$$3.79\left(0.0955+\frac{3750}{45514.8\times 9.8}\right)-0.069$$

Multiply 45514.8 and 9.8 to get 446045.04.

$$3.79\left(0.0955+\frac{3750}{446045.04}\right)-0.069$$

Expand \frac{3750}{446045.04} by multiplying both numerator and the denominator by 100.

$$3.79\left(0.0955+\frac{375000}{44604504}\right)-0.069$$

Reduce the fraction \frac{375000}{44604504} to lowest terms by extracting and canceling out 24.

$$3.79\left(0.0955+\frac{15625}{1858521}\right)-0.069$$

Convert decimal number 0.0955 to fraction \frac{955}{10000}. Reduce the fraction \frac{955}{10000} to lowest terms by extracting and canceling out 5.

$$3.79\left(\frac{191}{2000}+\frac{15625}{1858521}\right)-0.069$$

Least common multiple of 2000 and 1858521 is 3717042000. Convert \frac{191}{2000} and \frac{15625}{1858521} to fractions with denominator 3717042000.

$$3.79\left(\frac{354977511}{3717042000}+\frac{31250000}{3717042000}\right)-0.069$$

Since \frac{354977511}{3717042000} and \frac{31250000}{3717042000} have the same denominator, add them by adding their numerators.

$$3.79\times \frac{354977511+31250000}{3717042000}-0.069$$

Add 354977511 and 31250000 to get 386227511.

$$3.79\times \frac{386227511}{3717042000}-0.069$$

Convert decimal number 3.79 to fraction \frac{379}{100}.

$$\frac{379}{100}\times \frac{386227511}{3717042000}-0.069$$

Multiply \frac{379}{100} times \frac{386227511}{3717042000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{379\times 386227511}{100\times 3717042000}-0.069$$

Do the multiplications in the fraction \frac{379\times 386227511}{100\times 3717042000}.

$$\frac{146380226669}{371704200000}-0.069$$

Convert decimal number 0.069 to fraction \frac{69}{1000}.

$$\frac{146380226669}{371704200000}-\frac{69}{1000}$$

Least common multiple of 371704200000 and 1000 is 371704200000. Convert \frac{146380226669}{371704200000} and \frac{69}{1000} to fractions with denominator 371704200000.

$$\frac{146380226669}{371704200000}-\frac{25647589800}{371704200000}$$

Since \frac{146380226669}{371704200000} and \frac{25647589800}{371704200000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{146380226669-25647589800}{371704200000}$$

Subtract 25647589800 from 146380226669 to get 120732636869.

$$\frac{120732636869}{371704200000}$$

Factor

$$\frac{103 \cdot 503 \cdot 13789 \cdot 13 ^ {2}}{3 \cdot 47 \cdot 269 \cdot 2 ^ {6} \cdot 5 ^ {5} \cdot 7 ^ {2}} = 0.32480837415611663$$