General

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Section 1.1 General

Subsection 1.1.1 Rounding in calculations

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,

that is, to the nearest 3rd digit to the right of the decimal point.

Subsection 1.1.2 Solving 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 = B C

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 .

To solve the equation

Z = \frac{X - M}{S}

for

X,

first multiply both sides of the equation by

S

to obtain

Z S = X - M

then add

M

to both sides to obtain

X = Z S + M .

Exercises 1.1.3 Solving equations practice problems

1.

Consider the equation

A = \frac{B C + D}{E} .

Solve for $D .$
Solve for $B .$
Solve for $E .$

Answer.

$D = A E - B C$
$B = \frac{A E - D}{C}$
$E = \frac{B C + D}{A}$