MFG Entering Expressions

Processing math: 100%

Skip to main content

$\require{cancel}\newcommand\degree[0]{^{\circ}} \newcommand\Ccancel[2][black]{\renewcommand\CancelColor{\color{#1}}\cancel{#2}} \newcommand{\alert}[1]{\boldsymbol{\color{magenta}{#1}}} \newcommand{\blert}[1]{\boldsymbol{\color{blue}{#1}}} \newcommand{\bluetext}[1]{\color{blue}{#1}} \delimitershortfall-1sp \newcommand\abs[1]{\left|#1\right|} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&}$

Section B.2 Entering Expressions

Subsection Parentheses

Order of Operations: The calculator follows the standard order of operations.

Example B.6.

Compute \(2+3\cdot 4\text{.}\) Press

\(2\,\) + \(\,3\,\) X \(\,4\) ENTER

Ans. \(14\)

Example B.7.

Compute \((2+3)\cdot4\text{.}\) Press

( \(\,2\,\) + \(\,3\,\) ) X \(\,4\) ENTER

Ans. \(20\)

Example B.8.

Compute \(\dfrac{1}{2\cdot 3} \text{.}\) Press

\(1 \,\boxed{\div} \) ( \(\,2\,\) X \(\,3\,\) ) ENTER

Ans. \(0.1666666667\)

Example B.9.

Compute \(\dfrac{1+3}{2} \text{.}\) Press

( \(1 \, \) + \(\,3\,\) ) \(\boxed{ \div } \,2\,\) ENTER

Ans. \(2\)

Subsection Exponents and Powers

Exponents: We use the caret key, ^ , to enter exponents or powers.

Example B.10.

Evaluate \(2^{10}\text{.}\)

\(2\) ^ \(10\) ENTER

Ans. \(1024\)

Squaring: There is a short-cut key for squaring,

$\boxed{x^2}\text{.}$

Example B.11.

Evaluate \(57^{2}\text{.}\)

\(57~\boxed{x^2}\,\) ENTER

Ans. \(3249\)

Fractional Exponents: Fractional exponents must be enclosed in parentheses!

Example B.12.

Evaluate \(8^{2/3}\text{.}\)

\(8\,\) ^ ( \(2 ~ \boxed{\div} \, 3 \,\) ) ENTER

Ans. \(4\)

Subsection Roots

Square Roots: We access the square root by pressing 2nd

$\boxed{x^2} \text{,}$ and the display shows

$\sqrt{}(\text{.}$ The calculator automatically gives an open parenthesis for the square root, but not a close parenthesis.

Example B.13.

Evaluate \(\sqrt{2} \text{.}\)

2nd \(\boxed{x^2} \,2\,\) ) ENTER

Ans. \(1.414213562\)

Example B.14.

Evaluate \(\sqrt{9+16} \text{.}\)

2nd \(\boxed{x^2} \,9+16\,\) ) ENTER

Ans. \(5\)

In the next example, note that we must enter ) at the end of the radicand to tell the calculator where the radical ends.

Example B.15.

Evaluate \(\sqrt{9}+16 \text{.}\)

2nd \(\boxed{x^2} \,9\) ) \({}+{}16\,\) ENTER

Ans. \(19\)

Cube Roots: For cube roots, we press MATH to open the Math menu and press

$4$ (see Figure B.16).

two GC settings — 🔗
Figure B.16.

Example B.17.

Compute \(\sqrt[3]{1728} \text{.}\)

MATH \(~4~\) \(\, 1728\,\) ) ENTER

Ans. \(12\)

For evaluating cube roots and square roots, ) can be omitted if there are no operations following the radical.

Other Roots: For

$n$ th roots, we press MATH to open the Math menu and press

$5$ (see Figure B.16a). The calculator symbol for

$n$ th roots,

$\sqrt[x]{~} \text{,}$ does not include an open parenthesis,(. If the radicand includes an operation, we must enclose it in parentheses.

Example B.18.

Compute \(\sqrt[10]{2\cdot 512} \text{.}\)

\(10\,\)MATH \(~5~\) ( \(2\) x \(512\) ) ENTER

Ans. \(2\)

Notice that we enter the index 10 before the radical symbol.

Subsection Absolute Value

TI calculators use

$abs (x)$ instead of

$\abs{x}$ to denote the absolute value of

$x\text{.}$ The absolute value function is the first entry in the MATH NUM menu (see Figure B.19). The calculator gives ( for the absolute value function, but not ).

GC Math NUM menu — 🔗
Figure B.19.

Example B.20.

Evaluate \(\dfrac{\abs{21\cdot 54 - 81}}{-9} \text{.}\)

MATH \(\boxed{\rightarrow}\) ENTER \(21\) X \(54\) - \(81\) ) \(\,\boxed{\div} \) (-) \(9\) ENTER

Ans. \(-117\)

Subsection Scientific Notation

The TI calculators display numbers in scientific notation when the numbers use too many digits to display.

Example B.21.

Compute \(123,456,789^2 \text{.}\) Enter

\(123456789 ~ \boxed{x^2}\) ENTER

Ans. \(1.524157875 \text{ E }16\)

This is how the calculator displays the number

$1.524157875 \times 10^{16}\text{.}$ Notice that the power

$10^{16}$ is displayed as

$\text{ E }16\text{.}$

To enter a number in scientific form, we use the key labeled EE, or 2nd ,.

Example B.22.

To enter \(3.26 \times 10^{18}\text{,}\) use the keying sequence

\(3.26\) 2nd , (-) \(18\) ENTER

Ans. \(3.26 \text{ E}\) \(-18\)

Troubleshooting.

GC syntax error screen — Figure B.23.

If your calculator gives you an error message like this, you may have made one of the following common mistakes:

Using the negative key, (-), when you wanted the subtraction key, -, or vice versa.
Omitting a ( or ). Each ( should have a matching ).

Press

$2$ to Go to the error, and see Editing Expressions B.3 below.