Solve 1/3*3.142*4.5^2*20

$$\frac { 1 } { 3 } \times 3.142 \times 4.5 ^ { 2 } \times 20$$

Evaluate

$$424.17$$

Solution Steps

Convert decimal number 3.142 to fraction \frac{3142}{1000}. Reduce the fraction \frac{3142}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}\times \frac{1571}{500}\times 4.5^{2}\times 20$$

Multiply \frac{1}{3} times \frac{1571}{500} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1571}{3\times 500}\times 4.5^{2}\times 20$$

Do the multiplications in the fraction \frac{1\times 1571}{3\times 500}.

$$\frac{1571}{1500}\times 4.5^{2}\times 20$$

Calculate 4.5 to the power of 2 and get 20.25.

$$\frac{1571}{1500}\times 20.25\times 20$$

Convert decimal number 20.25 to fraction \frac{2025}{100}. Reduce the fraction \frac{2025}{100} to lowest terms by extracting and canceling out 25.

$$\frac{1571}{1500}\times \frac{81}{4}\times 20$$

Multiply \frac{1571}{1500} times \frac{81}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1571\times 81}{1500\times 4}\times 20$$

Do the multiplications in the fraction \frac{1571\times 81}{1500\times 4}.

$$\frac{127251}{6000}\times 20$$

Reduce the fraction \frac{127251}{6000} to lowest terms by extracting and canceling out 3.

$$\frac{42417}{2000}\times 20$$

Express \frac{42417}{2000}\times 20 as a single fraction.

$$\frac{42417\times 20}{2000}$$

Multiply 42417 and 20 to get 848340.

$$\frac{848340}{2000}$$

Reduce the fraction \frac{848340}{2000} to lowest terms by extracting and canceling out 20.

$$\frac{42417}{100}$$

Factor

$$\frac{1571 \cdot 3 ^ {3}}{2 ^ {2} \cdot 5 ^ {2}} = 424\frac{17}{100} = 424.17$$