Solve 1/33.14*0.16(0.2^2+0.08^2+0.2*0.08)

$$\frac{ 1 }{ 3 } 3.14 \cdot 0.16( { 0.2 }^{ 2 } + { 0.08 }^{ 2 } +0.2 \cdot 0.08)$$

Evaluate

$$0.01044992$$

Solution Steps

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}\times \frac{157}{50}\times 0.16\left(0.2^{2}+0.08^{2}+0.2\times 0.08\right)$$

Multiply \frac{1}{3} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 157}{3\times 50}\times 0.16\left(0.2^{2}+0.08^{2}+0.2\times 0.08\right)$$

Do the multiplications in the fraction \frac{1\times 157}{3\times 50}.

$$\frac{157}{150}\times 0.16\left(0.2^{2}+0.08^{2}+0.2\times 0.08\right)$$

Convert decimal number 0.16 to fraction \frac{16}{100}. Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$\frac{157}{150}\times \frac{4}{25}\left(0.2^{2}+0.08^{2}+0.2\times 0.08\right)$$

Multiply \frac{157}{150} times \frac{4}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{157\times 4}{150\times 25}\left(0.2^{2}+0.08^{2}+0.2\times 0.08\right)$$

Do the multiplications in the fraction \frac{157\times 4}{150\times 25}.

$$\frac{628}{3750}\left(0.2^{2}+0.08^{2}+0.2\times 0.08\right)$$

Reduce the fraction \frac{628}{3750} to lowest terms by extracting and canceling out 2.

$$\frac{314}{1875}\left(0.2^{2}+0.08^{2}+0.2\times 0.08\right)$$

Calculate 0.2 to the power of 2 and get 0.04.

$$\frac{314}{1875}\left(0.04+0.08^{2}+0.2\times 0.08\right)$$

Calculate 0.08 to the power of 2 and get 0.0064.

$$\frac{314}{1875}\left(0.04+0.0064+0.2\times 0.08\right)$$

Add 0.04 and 0.0064 to get 0.0464.

$$\frac{314}{1875}\left(0.0464+0.2\times 0.08\right)$$

Multiply 0.2 and 0.08 to get 0.016.

$$\frac{314}{1875}\left(0.0464+0.016\right)$$

Add 0.0464 and 0.016 to get 0.0624.

$$\frac{314}{1875}\times 0.0624$$

Convert decimal number 0.0624 to fraction \frac{624}{10000}. Reduce the fraction \frac{624}{10000} to lowest terms by extracting and canceling out 16.

$$\frac{314}{1875}\times \frac{39}{625}$$

Multiply \frac{314}{1875} times \frac{39}{625} by multiplying numerator times numerator and denominator times denominator.

$$\frac{314\times 39}{1875\times 625}$$

Do the multiplications in the fraction \frac{314\times 39}{1875\times 625}.

$$\frac{12246}{1171875}$$

Reduce the fraction \frac{12246}{1171875} to lowest terms by extracting and canceling out 3.

$$\frac{4082}{390625}$$

Factor

$$\frac{2 \cdot 13 \cdot 157}{5 ^ {8}} = 0.01044992$$