Solve frac{0.013^2*1+0.009^2*7+0.005^2*9+0.0017^2*53+{0.0022}^2*30+{0.0062}^2*12+{left(0.010right)}^2*7+{0.0142}^2*1}{120}

$$\frac{ { 0.013 }^{ 2 } \times 1+ { 0.009 }^{ 2 } \times 7+ { 0.005 }^{ 2 } \times 9+ { 0.0017 }^{ 2 } \times 53+ { 0.0022 }^{ 2 } \times 30+ { 0.0062 }^{ 2 } \times 12+ { \left(0.010 \right) }^{ 2 } \times 7+ { 0.0142 }^{ 2 } \times 1 }{ 120 }$$

Evaluate

$$\frac{262229}{12000000000}\approx 0.000021852$$

Solution Steps

Calculate 0.013 to the power of 2 and get 0.000169.

$$\frac{0.000169\times 1+0.009^{2}\times 7+0.005^{2}\times 9+0.0017^{2}\times 53+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Multiply 0.000169 and 1 to get 0.000169.

$$\frac{0.000169+0.009^{2}\times 7+0.005^{2}\times 9+0.0017^{2}\times 53+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Calculate 0.009 to the power of 2 and get 0.000081.

$$\frac{0.000169+0.000081\times 7+0.005^{2}\times 9+0.0017^{2}\times 53+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Multiply 0.000081 and 7 to get 0.000567.

$$\frac{0.000169+0.000567+0.005^{2}\times 9+0.0017^{2}\times 53+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Add 0.000169 and 0.000567 to get 0.000736.

$$\frac{0.000736+0.005^{2}\times 9+0.0017^{2}\times 53+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Calculate 0.005 to the power of 2 and get 0.000025.

$$\frac{0.000736+0.000025\times 9+0.0017^{2}\times 53+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Multiply 0.000025 and 9 to get 0.000225.

$$\frac{0.000736+0.000225+0.0017^{2}\times 53+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Add 0.000736 and 0.000225 to get 0.000961.

$$\frac{0.000961+0.0017^{2}\times 53+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Calculate 0.0017 to the power of 2 and get 0.00000289.

$$\frac{0.000961+0.00000289\times 53+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Multiply 0.00000289 and 53 to get 0.00015317.

$$\frac{0.000961+0.00015317+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Add 0.000961 and 0.00015317 to get 0.00111417.

$$\frac{0.00111417+0.0022^{2}\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Calculate 0.0022 to the power of 2 and get 0.00000484.

$$\frac{0.00111417+0.00000484\times 30+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Multiply 0.00000484 and 30 to get 0.0001452.

$$\frac{0.00111417+0.0001452+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Add 0.00111417 and 0.0001452 to get 0.00125937.

$$\frac{0.00125937+0.0062^{2}\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Calculate 0.0062 to the power of 2 and get 0.00003844.

$$\frac{0.00125937+0.00003844\times 12+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Multiply 0.00003844 and 12 to get 0.00046128.

$$\frac{0.00125937+0.00046128+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Add 0.00125937 and 0.00046128 to get 0.00172065.

$$\frac{0.00172065+0.01^{2}\times 7+0.0142^{2}\times 1}{120}$$

Calculate 0.01 to the power of 2 and get 0.0001.

$$\frac{0.00172065+0.0001\times 7+0.0142^{2}\times 1}{120}$$

Multiply 0.0001 and 7 to get 0.0007.

$$\frac{0.00172065+0.0007+0.0142^{2}\times 1}{120}$$

Add 0.00172065 and 0.0007 to get 0.00242065.

$$\frac{0.00242065+0.0142^{2}\times 1}{120}$$

Calculate 0.0142 to the power of 2 and get 0.00020164.

$$\frac{0.00242065+0.00020164\times 1}{120}$$

Multiply 0.00020164 and 1 to get 0.00020164.

$$\frac{0.00242065+0.00020164}{120}$$

Add 0.00242065 and 0.00020164 to get 0.00262229.

$$\frac{0.00262229}{120}$$

Expand \frac{0.00262229}{120} by multiplying both numerator and the denominator by 100000000.

$$\frac{262229}{12000000000}$$

Factor

$$\frac{11 \cdot 31 \cdot 769}{3 \cdot 2 ^ {11} \cdot 5 ^ {9}} = 2.1852416666666667 \times 10^{-5}$$