## SectionB.2Entering Expressions

### SubsectionParentheses

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

###### ExampleB.6

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

$2\,$ +  $\,3\,$ X  $\,4$ ENTER

Ans. $14$

###### ExampleB.7

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

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

Ans. $20$

###### ExampleB.8

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

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

Ans. $0.1666666667$

###### ExampleB.9

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

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

Ans. $2$

### SubsectionExponents and Powers

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

###### ExampleB.10

Evaluate $2^{10}\text{.}$

$2$  ^  $10$ ENTER

Ans. $1024$

Squaring: There is a short-cut key for squaring, $\boxed{x^2}\text{.}$

###### ExampleB.11

Evaluate $57^{2}\text{.}$

$57~\boxed{x^2}\,$ ENTER

Ans. $3249$

Fractional Exponents: Fractional exponents must be enclosed in parentheses!

###### ExampleB.12

Evaluate $8^{2/3}\text{.}$

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

Ans. $4$

### SubsectionRoots

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.

###### ExampleB.13

Evaluate $\sqrt{2} \text{.}$

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

Ans. $1.414213562$

###### ExampleB.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.

###### ExampleB.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).

###### ExampleB.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.

###### ExampleB.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.

### SubsectionAbsolute 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 ).

###### ExampleB.20

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

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

Ans. $-117$

### SubsectionScientific Notation

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

###### ExampleB.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  ,.

###### ExampleB.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

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.