Solve frac{(0.55)^{2}+(0.07)^2+(0.027)^2}{(0.055)^2+(0.007)^2}=?

$$\frac { ( 0.55 ) ^ { 2 } + ( 0.07 ) ^ { 2 } + ( 0.027 ) ^ { 2 } } { ( 0.055 ) ^ { 2 } + ( 0.007 ) ^ { 2 } } = ?$$

Evaluate

$$\frac{308129}{3074}\approx 100.237150293$$

Solution Steps

Calculate 0.55 to the power of 2 and get 0.3025.

$$\frac{0.3025+0.07^{2}+0.027^{2}}{0.055^{2}+0.007^{2}}$$

Calculate 0.07 to the power of 2 and get 0.0049.

$$\frac{0.3025+0.0049+0.027^{2}}{0.055^{2}+0.007^{2}}$$

Add 0.3025 and 0.0049 to get 0.3074.

$$\frac{0.3074+0.027^{2}}{0.055^{2}+0.007^{2}}$$

Calculate 0.027 to the power of 2 and get 0.000729.

$$\frac{0.3074+0.000729}{0.055^{2}+0.007^{2}}$$

Add 0.3074 and 0.000729 to get 0.308129.

$$\frac{0.308129}{0.055^{2}+0.007^{2}}$$

Calculate 0.055 to the power of 2 and get 0.003025.

$$\frac{0.308129}{0.003025+0.007^{2}}$$

Calculate 0.007 to the power of 2 and get 0.000049.

$$\frac{0.308129}{0.003025+0.000049}$$

Add 0.003025 and 0.000049 to get 0.003074.

$$\frac{0.308129}{0.003074}$$

Expand \frac{0.308129}{0.003074} by multiplying both numerator and the denominator by 1000000.

$$\frac{308129}{3074}$$

Factor

$$\frac{308129}{2 \cdot 29 \cdot 53} = 100\frac{729}{3074} = 100.23715029277814$$