## Scientific Notation

Scientific Notation

A number is written in scientific notation when it is expressed in the form

Where 1 ,and n is an integer.

## Converting to Scientific Notation

Converting to Scientific Notation

Step 1 :- Position the decimal point. Place a caret, ^, to the right of the

first nonzero digit, where the decimal point will be placed.

Step 2:- Determine the numeral for the exponent. Count the number

of digits from the decimal point to the caret. This number gives

the absolute value of the exponent on 10.

Step 3:- Determine the sign for the exponent. Decide whether multiplying

by 10nshould make the result of Step 1 larger or smaller. The

exponent should be positive to make the result larger; it should

be negative to make the result smaller.

Converting from Scientific Notation

Multiplying a number by a positive power of 10 makes the number larger,

so move the decimal point to the right n places if n is positive in 10n.

Multiplying by a negative power of 10 makes a number smaller, so

move the decimal point to the left places if │n│ is negative.

If n is 0, leave the decimal point where it is.

## Use function notation

Use function notation

When a function f is defined with a rule or an equation using x and y for the independent and dependent variables, we say “y is a function of x” to emphasize that y depends on x. We

use the notation

y = f (x),

called function notation, to express this and read f (x) as “f of x.” (In this special notation the parentheses do not indicate multiplication.) The letter f stands for function. For example, if y = 9x – 5, we can name this function f and write

f (x) = 9x –  5.

Note that f (x) is just another name for the dependent variable y. For example, if y = f (x) = 9x – 5 and x = 2, then we find y, or f (2), by replacing x with 2.

y  =  f (2) = 9 . 2 – 5

= 18 – 5

= 13.

For function f, the statement “if x = 2, then y = 13” is represented by the ordered pair (2, 13) and is abbreviated with function notation as

f (2) = 13.

Read f (2) as “f of 2” or “f at 2.” Also,

## Write sets using set notation

Write sets using set notation

A set is a collection of objects called the elements or members of the set. In algebra, the elements of a set are usually numbers. Set braces, { }, are used to enclose the elements.

For example, 2 is an element of the set {1, 2, 3}. Since we can count the number of elements in the set {1, 2, 3}, it is a finite set.

In our study of algebra, we refer to certain sets of numbers by name. The set

N 5 {1, 2, 3, 4, 5, 6, . . . } is called the

natural numbers or the counting numbers. The three dots

show that the list continues in the same pattern indefinitely. We cannot list

all of the elements of the set of natural numbers, so it is an infinite set.

When 0 is included with the set of natural numbers, we have the set of

whole numbers, written W 5 {0, 1, 2, 3, 4, 5, 6, . . . }.

A set containing no elements, such as the set of whole numbers less than 0,

is called the empty set, or null set, usually written .

Caution

Do not write {ø } for the empty set; { ø } is a set with one element, . Use

only the notation for the empty set.

In algebra, letters called variables are often used to represent numbers

or to define sets of numbers. For example,

{x | x is a natural number between 3 and 15}

(read “the set of all elements x such that x is a natural number between 3 and

15”) defines the set

{4, 5, 6, 7, . . . , 14}.

The notation {x | x is a natural number between 3 and 15} is an example

of set-builder notation.

{ x | x has property P }

the set of all elements x such that x has a given property P