## Posts Tagged ‘notation’

## 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 10^{n}should 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 10* ^{n}*.

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 **= 9

*x*– 5

*,*we can name this function

*f*and write

*f ***(***x***) **= 9*x – * 5.

Note that *f ***(***x***) **** is just another name for the dependent variable y. **For example, if

*y*=

*f*(

*x*) = 9

*x*– 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*