Solve 0.04/1.1+0.9*0.07+0.06*0.23/1.1^2

$$\frac { 0.04 } { 1.1 } + \frac { 0.9 \cdot 0.07 + 0.06 \cdot 0.23 } { 1.1 ^ { 2 } }$$

Evaluate

$$\frac{302}{3025}\approx 0.099834711$$

Solution Steps

Expand \frac{0.04}{1.1} by multiplying both numerator and the denominator by 100.

$$\frac{4}{110}+\frac{0.9\times 0.07+0.06\times 0.23}{1.1^{2}}$$

Reduce the fraction \frac{4}{110} to lowest terms by extracting and canceling out 2.

$$\frac{2}{55}+\frac{0.9\times 0.07+0.06\times 0.23}{1.1^{2}}$$

Multiply 0.9 and 0.07 to get 0.063.

$$\frac{2}{55}+\frac{0.063+0.06\times 0.23}{1.1^{2}}$$

Multiply 0.06 and 0.23 to get 0.0138.

$$\frac{2}{55}+\frac{0.063+0.0138}{1.1^{2}}$$

Add 0.063 and 0.0138 to get 0.0768.

$$\frac{2}{55}+\frac{0.0768}{1.1^{2}}$$

Calculate 1.1 to the power of 2 and get 1.21.

$$\frac{2}{55}+\frac{0.0768}{1.21}$$

Expand \frac{0.0768}{1.21} by multiplying both numerator and the denominator by 10000.

$$\frac{2}{55}+\frac{768}{12100}$$

Reduce the fraction \frac{768}{12100} to lowest terms by extracting and canceling out 4.

$$\frac{2}{55}+\frac{192}{3025}$$

Least common multiple of 55 and 3025 is 3025. Convert \frac{2}{55} and \frac{192}{3025} to fractions with denominator 3025.

$$\frac{110}{3025}+\frac{192}{3025}$$

Since \frac{110}{3025} and \frac{192}{3025} have the same denominator, add them by adding their numerators.

$$\frac{110+192}{3025}$$

Add 110 and 192 to get 302.

$$\frac{302}{3025}$$

Factor

$$\frac{2 \cdot 151}{5 ^ {2} \cdot 11 ^ {2}} = 0.09983471074380165$$