Page 312 - Theory and Problems of BEGINNING CHEMISTRY

APP.] SCIENTIFIC CALCULATIONS 301

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corresponding to the exponent. For example, to enter 4 × 10 into the calculator, press
EE
4EE5 or 4 EXP 5
Do not press the times × keyorthe 1 and 0 keys when entering an exponential number! The EE or EXP key
stands for “times 10 to the power.” For simplicity, we will use EXP to mean either EXP or EE from this point on.
If the coefficient is negative, press the +/− key before the EXP key. If the exponent is negative, press the
+/− key after the EXP key.

−5
EXAMPLE A.18. What keys should be pressed to enter the number −4.44 × 10 ?
Ans. 4 . 4 4 +/− EXP 5 +/−
or 4 . 4 4 +/− EXP +/− 5

EXAMPLE A.19. What value will be displayed if you enter the following sequence of keystrokes?

4 . 4 4 × 1 0 EXP 5 =
Ans. These keystrokes perform the calculation
5
4.44 × (10 × 10 ) =
6
The resulting value will be 4.44 × 10 (which might be displayed in floating-point format as 4 440 000). These
5
keystrokes instruct the calculator to multiply 4.44 by 10 × 10 , which yields a value 10 times larger than was
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intended if you wanted to enter 4.44 × 10 .
EXAMPLE A.20. A student presses the following sequence of keys: to get the value of the quotient
4 × 10 7
4 × 10 7

4 × 1 0 EXP 7 ÷ 4 × 1 0 EXP 7 =
What value is displayed on the calculator as a result?
16
7
8
Ans. The result is 1 × 10 . The calculator divides 4 × 10 by 4, then multiplies that answer by 10 times 10 . (See the
precedence rules in Table A-1.) This answer is wrong because any number divided by itself should give an answer
of 1. (You should always check to see if your answer is reasonable.)
EXAMPLE A.21. What keystrokes should the student have used to get the correct result in Example A.20?

Ans. 4 EXP 7 ÷ 4 EXP 7 =
The precedence rules are not invoked for this sequence of keystrokes, since only one operation, division, is done.

Some calculators display answers in decimal notation unless they are programmed to display them in
scientific notation. If a number is too large to fit on the display, such a calculator will use scientific notation
automatically. To get a display in scientific notation for a reasonably sized decimal number, press the SCI key
or an equivalent key, if available. (See your instruction booklet.) If automatic conversion is not available on your
calculator, you can multiply the decimal value by 1 × 10 10 (if the number is greater than 1) or 1 × 10 −10 (if
the number is less than 1), which forces the display automatically into scientific notation. Then you mentally
subtract or add 10 to the resulting exponent.

The Reciprocal Key
The reciprocal of a number is 1 divided by the number. It has the same number of significant digits as the
number itself. For example, the reciprocal of 5.00 is 0.200. A number times its reciprocal is equal to 1.