Roundoff errors made at intermediate steps of a multi-step calculation tend to become magnified. For this reason, do not round off numbers until the final step of a calculation, unless you are simply making a rough estimate. If you must round, keep lots of digits. A rule of thumb is to round to the nearest \(0.001\text{,}\) that is, to the nearest 3rd digit to the right of the decimal point.
Subsection1.1.2Solving equations
To solve a given equation for a particular quantity \(X\) means to manipulate the given equation into a new equation where \(X\) is all by itself on one side. For example, the equation \(A=BC\) can be solved for \(C\) by dividing both sides of the equation by \(B\) (this is valid as long as \(B\) is not zero). This manipulation results in the new equation \(C=\frac{A}{B}\) which is solved for \(C\text{.}\)
To solve the equation
\begin{equation*}
Z=\frac{X-M}{S}
\end{equation*}
for \(X\text{,}\) first multiply both sides of the equation by \(S\) to obtain
\begin{equation*}
ZS = X-M
\end{equation*}
then add \(M\) to both sides to obtain
\begin{equation*}
X=ZS+M.
\end{equation*}
Exercises1.1.3Solving equations practice problems
1.
Consider the equation \(A = \frac{BC + D}{E}\text{.}\)
