Solve (0.3/100^2+0.2/110^2)

$$( \frac{ 0.3 }{ { 100 }^{ 2 } } + \frac{ 0.2 }{ { 110 }^{ 2 } } )$$

Evaluate

$$\frac{563}{12100000}\approx 0.000046529$$

Solution Steps

Calculate 100 to the power of 2 and get 10000.

$$\frac{0.3}{10000}+\frac{0.2}{110^{2}}$$

Expand \frac{0.3}{10000} by multiplying both numerator and the denominator by 10.

$$\frac{3}{100000}+\frac{0.2}{110^{2}}$$

Calculate 110 to the power of 2 and get 12100.

$$\frac{3}{100000}+\frac{0.2}{12100}$$

Expand \frac{0.2}{12100} by multiplying both numerator and the denominator by 10.

$$\frac{3}{100000}+\frac{2}{121000}$$

Reduce the fraction \frac{2}{121000} to lowest terms by extracting and canceling out 2.

$$\frac{3}{100000}+\frac{1}{60500}$$

Least common multiple of 100000 and 60500 is 12100000. Convert \frac{3}{100000} and \frac{1}{60500} to fractions with denominator 12100000.

$$\frac{363}{12100000}+\frac{200}{12100000}$$

Since \frac{363}{12100000} and \frac{200}{12100000} have the same denominator, add them by adding their numerators.

$$\frac{363+200}{12100000}$$

Add 363 and 200 to get 563.

$$\frac{563}{12100000}$$

Factor

$$\frac{563}{2 ^ {5} \cdot 5 ^ {5} \cdot 11 ^ {2}} = 4.652892561983471 \times 10^{-5}$$