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

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:

  1. Using the negative key, (-), when you wanted the subtraction key, -, or vice versa.

  2. Omitting a ( or ). Each ( should have a matching ).

Press \(2\) to Go to the error, and see Editing Expressions B.3 below.