Solve frac{(0.03)^{2}+(0.02)^2+(-0.01)^2+(-0.03)^2+(0.01)^2}{6}

$$\frac { ( 0.03 ) ^ { 2 } + ( 0.02 ) ^ { 2 } + ( - 0.01 ) ^ { 2 } + ( - 0.03 ) ^ { 2 } + ( 0.01 ) ^ { 2 } } { 6 }$$

Evaluate

$$0.0004$$

Solution Steps

Calculate 0.03 to the power of 2 and get 0.0009.

$$\frac{0.0009+0.02^{2}+\left(-0.01\right)^{2}+\left(-0.03\right)^{2}+0.01^{2}}{6}$$

Calculate 0.02 to the power of 2 and get 0.0004.

$$\frac{0.0009+0.0004+\left(-0.01\right)^{2}+\left(-0.03\right)^{2}+0.01^{2}}{6}$$

Add 0.0009 and 0.0004 to get 0.0013.

$$\frac{0.0013+\left(-0.01\right)^{2}+\left(-0.03\right)^{2}+0.01^{2}}{6}$$

Calculate -0.01 to the power of 2 and get 0.0001.

$$\frac{0.0013+0.0001+\left(-0.03\right)^{2}+0.01^{2}}{6}$$

Add 0.0013 and 0.0001 to get 0.0014.

$$\frac{0.0014+\left(-0.03\right)^{2}+0.01^{2}}{6}$$

Calculate -0.03 to the power of 2 and get 0.0009.

$$\frac{0.0014+0.0009+0.01^{2}}{6}$$

Add 0.0014 and 0.0009 to get 0.0023.

$$\frac{0.0023+0.01^{2}}{6}$$

Calculate 0.01 to the power of 2 and get 0.0001.

$$\frac{0.0023+0.0001}{6}$$

Add 0.0023 and 0.0001 to get 0.0024.

$$\frac{0.0024}{6}$$

Expand \frac{0.0024}{6} by multiplying both numerator and the denominator by 10000.

$$\frac{24}{60000}$$

Reduce the fraction \frac{24}{60000} to lowest terms by extracting and canceling out 24.

$$\frac{1}{2500}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 5 ^ {4}} = 0.0004$$