Solve frac{4*3.14^{2}}{1.9842^2}*2*10^-4+8*3.14^2*0.9881/1.9842^3*0.0002

$$\frac { 4 \times 3.14 ^ { 2 } } { 1.9842 ^ { 2 } } \cdot 2 \times 10 ^ { - 4 } + \frac { 8 \times 3.14 ^ { 2 } \times 0.9881 } { 1.9842 ^ { 3 } } \times 0.0002$$

Evaluate

$$\frac{3904795984}{976486736961}\approx 0.003998821$$

Solution Steps

Calculate 3.14 to the power of 2 and get 9.8596.

$$\frac{4\times 9.8596}{1.9842^{2}}\times 2\times 10^{-4}+\frac{8\times 3.14^{2}\times 0.9881}{1.9842^{3}}\times 0.0002$$

Multiply 4 and 9.8596 to get 39.4384.

$$\frac{39.4384}{1.9842^{2}}\times 2\times 10^{-4}+\frac{8\times 3.14^{2}\times 0.9881}{1.9842^{3}}\times 0.0002$$

Calculate 1.9842 to the power of 2 and get 3.93704964.

$$\frac{39.4384}{3.93704964}\times 2\times 10^{-4}+\frac{8\times 3.14^{2}\times 0.9881}{1.9842^{3}}\times 0.0002$$

Expand \frac{39.4384}{3.93704964} by multiplying both numerator and the denominator by 100000000.

$$\frac{3943840000}{393704964}\times 2\times 10^{-4}+\frac{8\times 3.14^{2}\times 0.9881}{1.9842^{3}}\times 0.0002$$

Reduce the fraction \frac{3943840000}{393704964} to lowest terms by extracting and canceling out 4.

$$\frac{985960000}{98426241}\times 2\times 10^{-4}+\frac{8\times 3.14^{2}\times 0.9881}{1.9842^{3}}\times 0.0002$$

Multiply \frac{985960000}{98426241} and 2 to get \frac{1971920000}{98426241}.

$$\frac{1971920000}{98426241}\times 10^{-4}+\frac{8\times 3.14^{2}\times 0.9881}{1.9842^{3}}\times 0.0002$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{1971920000}{98426241}\times \frac{1}{10000}+\frac{8\times 3.14^{2}\times 0.9881}{1.9842^{3}}\times 0.0002$$

Multiply \frac{1971920000}{98426241} and \frac{1}{10000} to get \frac{197192}{98426241}.

$$\frac{197192}{98426241}+\frac{8\times 3.14^{2}\times 0.9881}{1.9842^{3}}\times 0.0002$$

Calculate 3.14 to the power of 2 and get 9.8596.

$$\frac{197192}{98426241}+\frac{8\times 9.8596\times 0.9881}{1.9842^{3}}\times 0.0002$$

Multiply 8 and 9.8596 to get 78.8768.

$$\frac{197192}{98426241}+\frac{78.8768\times 0.9881}{1.9842^{3}}\times 0.0002$$

Multiply 78.8768 and 0.9881 to get 77.93816608.

$$\frac{197192}{98426241}+\frac{77.93816608}{1.9842^{3}}\times 0.0002$$

Calculate 1.9842 to the power of 3 and get 7.811893895688.

$$\frac{197192}{98426241}+\frac{77.93816608}{7.811893895688}\times 0.0002$$

Expand \frac{77.93816608}{7.811893895688} by multiplying both numerator and the denominator by 1000000000000.

$$\frac{197192}{98426241}+\frac{77938166080000}{7811893895688}\times 0.0002$$

Reduce the fraction \frac{77938166080000}{7811893895688} to lowest terms by extracting and canceling out 8.

$$\frac{197192}{98426241}+\frac{9742270760000}{976486736961}\times 0.0002$$

Multiply \frac{9742270760000}{976486736961} and 0.0002 to get \frac{1948454152}{976486736961}.

$$\frac{197192}{98426241}+\frac{1948454152}{976486736961}$$

Add \frac{197192}{98426241} and \frac{1948454152}{976486736961} to get \frac{3904795984}{976486736961}.

$$\frac{3904795984}{976486736961}$$

Factor

$$\frac{9901 \cdot 2 ^ {4} \cdot 157 ^ {2}}{3 ^ {3} \cdot 3307 ^ {3}} = 0.0039988213215802785$$