Solve =(0.02)^3*0.8/(0.02)^3*0.8+(0.9)^3*0.15+(0.1)^3*0.05

$$= \frac { ( 0.02 ) ^ { 3 } \times 0.8 } { ( 0.02 ) ^ { 3 } \times 0.8 + ( 0.9 ) ^ { 3 } \times 0.15 + ( 0.1 ) ^ { 3 } \times 0.05 }$$

Evaluate

$$\frac{4}{68379}\approx 0.000058497$$

Solution Steps

Calculate 0.02 to the power of 3 and get 0.000008.

$$\frac{0.000008\times 0.8}{0.02^{3}\times 0.8+0.9^{3}\times 0.15+0.1^{3}\times 0.05}$$

Multiply 0.000008 and 0.8 to get 0.0000064.

$$\frac{0.0000064}{0.02^{3}\times 0.8+0.9^{3}\times 0.15+0.1^{3}\times 0.05}$$

Calculate 0.02 to the power of 3 and get 0.000008.

$$\frac{0.0000064}{0.000008\times 0.8+0.9^{3}\times 0.15+0.1^{3}\times 0.05}$$

Multiply 0.000008 and 0.8 to get 0.0000064.

$$\frac{0.0000064}{0.0000064+0.9^{3}\times 0.15+0.1^{3}\times 0.05}$$

Calculate 0.9 to the power of 3 and get 0.729.

$$\frac{0.0000064}{0.0000064+0.729\times 0.15+0.1^{3}\times 0.05}$$

Multiply 0.729 and 0.15 to get 0.10935.

$$\frac{0.0000064}{0.0000064+0.10935+0.1^{3}\times 0.05}$$

Add 0.0000064 and 0.10935 to get 0.1093564.

$$\frac{0.0000064}{0.1093564+0.1^{3}\times 0.05}$$

Calculate 0.1 to the power of 3 and get 0.001.

$$\frac{0.0000064}{0.1093564+0.001\times 0.05}$$

Multiply 0.001 and 0.05 to get 0.00005.

$$\frac{0.0000064}{0.1093564+0.00005}$$

Add 0.1093564 and 0.00005 to get 0.1094064.

$$\frac{0.0000064}{0.1094064}$$

Expand \frac{0.0000064}{0.1094064} by multiplying both numerator and the denominator by 10000000.

$$\frac{64}{1094064}$$

Reduce the fraction \frac{64}{1094064} to lowest terms by extracting and canceling out 16.

$$\frac{4}{68379}$$

Factor

$$\frac{2 ^ {2}}{3 \cdot 23 \cdot 991} = 5.849749192003392 \times 10^{-5}$$