18
Number Notations, Arithmetical Operations, and Calculators
SOME OTHER BASIC MATH OPERATIONS
There are some additional math operations that you should be able to handle
easily, either with calculators or with log tables. Three of these are discussed
here.
Reciprocals
The quotient that results when any number is divided into one is said to be the
reciprocal of that number. It is a common value that can be found on any
calculator by making the required division, but almost every calculator has a
"reciprocal" key (usually labeled \lx) that makes it even easier. All you do is
enter through the keyboard the number whose reciprocal you want; then press
the \lx key, and the reciprocal appears in the lighted display. You should learn
to take advantage of this key; it is very useful. With your own calculator verify
that 1/83.6 = 0.01196; 1/0.00000297 = 3.367 x 10
5
; and 1/6.059 x 10
7 = 1.650x
to8 .
Powers
We have discussed at length the usefulness of powers of 10 as part of scientific
notation, but many practical problems involve the powers of other numbers.
For example, the area of a circle involves the square of the radius, and the
volume of a sphere involves the cube of the radius. Nearly every calculator
yields the square of a number when you simply enter the number through the
keyboard and then press the x
2 key; the square appears in the lighted display.
For powers other than 2 you will need to use the y
x key, as follows.
1. Enter through the keyboard the number you wish to raise to some
power.
2. a. Press the ENTER key (on an HP-type calculator),
b. Press the \* key (on a Tl-type calculator).
3. Enter through the keyboard the power to which you wish to raise the
number, but ignore the minus sign if the exponent is a negative number.
The number need not be an integer, and it may be less than one as well
as larger than one.
4. If the power is negative, press the "change sign" key (common key
symbols are CHS and +/-); don't press the — key.
5. a. Press the y* key (on an HP-type calculator),
b. Press the = key (on a Tl-type calculator).
6. The answer will be found in the lighted display.
Number Notations, Arithmetical Operations, and Calculators
SOME OTHER BASIC MATH OPERATIONS
There are some additional math operations that you should be able to handle
easily, either with calculators or with log tables. Three of these are discussed
here.
Reciprocals
The quotient that results when any number is divided into one is said to be the
reciprocal of that number. It is a common value that can be found on any
calculator by making the required division, but almost every calculator has a
"reciprocal" key (usually labeled \lx) that makes it even easier. All you do is
enter through the keyboard the number whose reciprocal you want; then press
the \lx key, and the reciprocal appears in the lighted display. You should learn
to take advantage of this key; it is very useful. With your own calculator verify
that 1/83.6 = 0.01196; 1/0.00000297 = 3.367 x 10
5
; and 1/6.059 x 10
7 = 1.650x
to8 .
Powers
We have discussed at length the usefulness of powers of 10 as part of scientific
notation, but many practical problems involve the powers of other numbers.
For example, the area of a circle involves the square of the radius, and the
volume of a sphere involves the cube of the radius. Nearly every calculator
yields the square of a number when you simply enter the number through the
keyboard and then press the x
2 key; the square appears in the lighted display.
For powers other than 2 you will need to use the y
x key, as follows.
1. Enter through the keyboard the number you wish to raise to some
power.
2. a. Press the ENTER key (on an HP-type calculator),
b. Press the \* key (on a Tl-type calculator).
3. Enter through the keyboard the power to which you wish to raise the
number, but ignore the minus sign if the exponent is a negative number.
The number need not be an integer, and it may be less than one as well
as larger than one.
4. If the power is negative, press the "change sign" key (common key
symbols are CHS and +/-); don't press the — key.
5. a. Press the y* key (on an HP-type calculator),
b. Press the = key (on a Tl-type calculator).
6. The answer will be found in the lighted display.