Evaluate 2.85*(35pi)/36

Problem

2.85⋅(35*π)/36

Solution

1. Convert the decimal 2.85 into a fraction to make simplification easier.

2.85=285/100

2. Simplify the fraction 285/100 by dividing both the numerator and denominator by their greatest common divisor, 5

285/100=57/20

3. Substitute the fraction back into the original expression.

57/20⋅(35*π)/36

4. Multiply the numerators and denominators.

(57⋅35*π)/(20⋅36)

5. Simplify the expression by canceling common factors. Divide 35 and 20 by 5 and divide 57 and 36 by 3

57/36=19/12

35/20=7/4

6. Calculate the final product of the simplified terms.

(19⋅7*π)/(4⋅12)=(133*π)/48

7. Convert to a decimal approximation if required, using π≈3.14159

(133⋅3.14159)/48≈8.7047

Final Answer

2.85⋅(35*π)/36=(133*π)/48

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