When I ask my calculator to divide 0.35 by ( 0.15 ) * ( 0.30 )^2 it gives me the result 0.21. The correct result should be about 26. What's going wrong?

Nov 7, 2016

The operator precedence rules used by the calculator have interpreted the expression you gave it in a different way from your intention.

Explanation:

The calculator has not understood your intention due to the way that it applies rules of operator precedence.

You can get it to understand what you want unambiguously by using parentheses around expressions you want to be evaluated first.

You are typing something like this into your calculator:

$0.35 \div \left(\textcolor{w h i t e}{.} 0.15 \textcolor{w h i t e}{.}\right) \times \left(\textcolor{w h i t e}{.} 0.30 \textcolor{w h i t e}{.}\right) \textcolor{w h i t e}{.} {\text{x}}^{2} =$

It is interpreting this expression as:

$\left(\frac{0.35}{0.15}\right) \cdot {\left(0.30\right)}^{2} = 0.21$

...performing the division before the multiplication.

You can force the calculator to delay doing the division by typing something like this:

$0.35 \div \left(\textcolor{w h i t e}{.} 0.25 \times 0.30 \textcolor{w h i t e}{.} {\text{x}}^{2} \textcolor{w h i t e}{.}\right) =$

which it will interpret as:

$\frac{0.35}{0.15 \cdot {0.30}^{2}} = 25. \overline{925} \approx 26$