Solve 0.2+1/6*0.3^3-0.1^3*1/6

$$0.2 + \frac { 1 } { 6 } \times 0.3 ^ { 3 } - 0.1 ^ { 3 } \times \frac { 1 } { 6 }$$

Evaluate

$$\frac{613}{3000}\approx 0.204333333$$

Solution Steps

Calculate 0.3 to the power of 3 and get 0.027.

$$0.2+\frac{1}{6}\times 0.027-0.1^{3}\times \frac{1}{6}$$

Convert decimal number 0.027 to fraction \frac{27}{1000}.

$$0.2+\frac{1}{6}\times \frac{27}{1000}-0.1^{3}\times \frac{1}{6}$$

Multiply \frac{1}{6} times \frac{27}{1000} by multiplying numerator times numerator and denominator times denominator.

$$0.2+\frac{1\times 27}{6\times 1000}-0.1^{3}\times \frac{1}{6}$$

Do the multiplications in the fraction \frac{1\times 27}{6\times 1000}.

$$0.2+\frac{27}{6000}-0.1^{3}\times \frac{1}{6}$$

Reduce the fraction \frac{27}{6000} to lowest terms by extracting and canceling out 3.

$$0.2+\frac{9}{2000}-0.1^{3}\times \frac{1}{6}$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}+\frac{9}{2000}-0.1^{3}\times \frac{1}{6}$$

Least common multiple of 5 and 2000 is 2000. Convert \frac{1}{5} and \frac{9}{2000} to fractions with denominator 2000.

$$\frac{400}{2000}+\frac{9}{2000}-0.1^{3}\times \frac{1}{6}$$

Since \frac{400}{2000} and \frac{9}{2000} have the same denominator, add them by adding their numerators.

$$\frac{400+9}{2000}-0.1^{3}\times \frac{1}{6}$$

Add 400 and 9 to get 409.

$$\frac{409}{2000}-0.1^{3}\times \frac{1}{6}$$

Calculate 0.1 to the power of 3 and get 0.001.

$$\frac{409}{2000}-0.001\times \frac{1}{6}$$

Convert decimal number 0.001 to fraction \frac{1}{1000}.

$$\frac{409}{2000}-\frac{1}{1000}\times \frac{1}{6}$$

Multiply \frac{1}{1000} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{409}{2000}-\frac{1\times 1}{1000\times 6}$$

Do the multiplications in the fraction \frac{1\times 1}{1000\times 6}.

$$\frac{409}{2000}-\frac{1}{6000}$$

Least common multiple of 2000 and 6000 is 6000. Convert \frac{409}{2000} and \frac{1}{6000} to fractions with denominator 6000.

$$\frac{1227}{6000}-\frac{1}{6000}$$

Since \frac{1227}{6000} and \frac{1}{6000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1227-1}{6000}$$

Subtract 1 from 1227 to get 1226.

$$\frac{1226}{6000}$$

Reduce the fraction \frac{1226}{6000} to lowest terms by extracting and canceling out 2.

$$\frac{613}{3000}$$

Factor

$$\frac{613}{3 \cdot 2 ^ {3} \cdot 5 ^ {3}} = 0.20433333333333334$$