Real Numbers
-Real Numbers are every number.
-Therefore, any number that you can find on the number line. -Real Numbers have two categories, rational and irrational.
Rational Numbers
-Any number that can be expressed as a repeating or terminating decimal is classified as a rational number Examples of Rational Numbers
6 is a rational number because it can be expressed as 6.0 and therefore it is a terminating decimal. -7 ½ is a rational number because it can be expressed as -7.5 which is a terminating decimal. Examples of Rational Numbers

Square root 25 is a rational number because it can be expressed as 5 or 5.0 and therefore it is a terminating decimal. 2.45 is a rational number because it is a repeating decimal. Irrational Numbers

-An irrational number is a number that cannot be written as a fraction of two integers. -Irrational numbers written as decimals are non-terminating and non-repeating. Note: if a whole number is not a perfect square, then its square root is an irrational number. Caution!

A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits. Examples of Irrational Numbers
Square root of 21 is an irrational number because it can Not be expressed as a terminating decimal. 0.62622622262222… is an irrational number because it cannot be expressed as a repeating decimal. Examples of Irrational Numbers

Π (pi)is an irrational number.

Subsets of Rational Numbers
-Natural numbers
-Whole numbers
-Integers
Natural Numbers
Natural Numbers are counting numbers from {1,2,3,4,5,…}
Whole Numbers
Whole numbers are counting numbers from {0,1,2,3,4,5,…}
Integers
Integers include the negative counting numbers: {…,-3,-2,-1,0,1,2,3…} What Does It Mean?
-The number line goes on forever.
-Every point on the line is a Real number.
-There are no gaps on the number line.
-Between the integers there are countless other numbers. Some of them are rational (fractions, terminating and repeating...

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Real World Radical Formulas
Janeth Mendiola
MAT222: Intermediate Algebra
Instructor Lalla Thompson
March 21, 2014
Real World Radical Formulas
Radical formulas are used in the real world in the fields such as finance, medicine, engineering, and physics to name a few. In the finance department they use it to find the interest, depreciation and compound interest. In medicine it can be used to calculate the Body Surface of an adult (BSA), in engineering it can be used to measure voltage. These formulas are vital and important not only in algebra but also as we can see in our day-to-day lives. This assignment requires that we find the capsizing screening value for the Tartan 4100, solve the formula for variable of d, and find the displacement in which the Tartan 4100 is safe for ocean sailing. The problem is broken down into three parts. The utilization of formulas will be used.
The problem and work will be on the left hand side and a description will be to the right of the work describing the steps taken to solve this assignment. The following words will be bold throughout the assignment to indicate that there is a clear understanding of their definition and use: radical, root, and variable. The assignment requires solving problem 103 on page 605 of our reading material. With the given information we will solve three different parts using the information given and using radical...

...In mathematics, a realnumber is a value that represents a quantity along a continuous line. The realnumbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356... the square root of two, an irrational algebraic number) and π (3.14159265..., a transcendental number). Realnumbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any realnumber can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include realnumbers as a special case.
These descriptions of the realnumbers are not sufficiently rigorous by the modern standards of pure mathematics. The discovery of a suitably rigorous definition of the realnumbers — indeed, the realization that a better definition was needed — was one of the most important developments of 19th century mathematics. The currently...

...Algebra 1, EOC Practice Items
Washington performance expectations assessed for purposes of graduation.
A1.1.A Select and justify functions and equations to model and solve problems.
1. Mrs. Morris gave her students this pattern of white tiles
She asked her students to write an equation to represent the number of white tiles, t, for any figure number, n.
Which equation represents the number of white tiles in the pattern?
A. t = n + 2
B. t = n + 4
C. t = 4n + 4
D. t = 4n + 8
2. Kesha is planning to rent a van for her trip to Mt. Rainier. Two of her friends each rented the same type of van from the same car rental company last week. This is what they told her:
John: “The cost of my rental was $240. The company charged me a certain amount per day and a certain amount per mile. I had the rental for five days and I drove it 200 miles.”
Katie: “The cost of my rental was only $100. I drove it for 100 miles and had it for two days.”
Kesha plans to get the same type of van that John and Katie had from the same car rental company. Kesha estimated her trip would be 250 miles, and she would have the vehicle for four days.
Let C = cost, M = miles, and D = days
Which equation could Kesha use to figure out how much her rental would cost?
A. C = 40.00M + 0.20D
B. C = 40.00D + 0.20M
C. C = 20.00M + 0.40D
D. C = 20.00D + 0.40M
3. Joey earned money over the...

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TUTORIAL: NUMBER SYSTEM
1. Determine whether each statement is true or false
a) Every counting number is an integer
b) Zero is a counting number
c) Negative six is greater than negative three
d) Some of the integers is natural numbers
2. List the number describe and graph them on the number line
a) The counting number smaller than 6
b) The integer between -3 and 3
3. Given S = {-3, 0,[pic], [pic], e, , 4, 8…}, identify the set of
(a) natural numbers (b) whole numbers (c) integers
(d) rational numbers (e) irrational numbers (f) realnumbers
4. Express each of the numbers as a quotient [pic]
(a) 0.7777…… (b) 2.7181818….
5. Write each of the following inequalities in interval notation and show them on the realnumber line.
(a) 2 < x < 6 (b) (5 < x < (1
(c) (3 ( x ( 7 (d) (2 < x ( 0
(e) x < 3 (f) x ( (1
(g) x ( (2 (h) (3 ( x < 2
6. Show each of the following intervals on the realnumber line.
(a) [(2, 3] (b) ((4, 4)
(c) (((, 5] (d) [(1, ()
(e) ((3, 6] (f) [(2, 3)
(g) ((2, 0) ( (3, 6) (h) [(6, 2) ( [(3, 7)
2 Evaluate
(a) [pic] (b) 27[pic] (c) [pic] (d) [pic]
(e) (0.36)[pic] (f) (2.56)[pic] (g) [pic] (h)...

... NUMBER SYSTEM
Definition
It defines how a number can be represented using distinct symbols. A number can be represented differently in different systems,
for instance the two number systems (2A) base 16 and (52) base 8 both refer to the same quantity though the representations are different.
When we type some letters or words, the computer translates them in numbers as computers can understand onlynumbers.
A computer can understand positional number system where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.
A value of each digit in a number can be determined using
The digit
The position of the digit in the number
The base of the number system (where base is defined as the total number of digits available in the number system).
1. Decimal Number System
The number system that we use in our day-to-day life is the decimal number system. Decimal number system has base 10 as it uses 10 digits from 0 to 9. In decimal number system, the successive positions to the left of the decimal point represent units, tens, hundreds, thousands and so on.
Each position represents a specific power of the base (10). For example, the...

...Historical Survey of Number Systems
Nikolai Weibull
1. Introduction
In a narrow, yet highly unspecific, sense, a number system is a way in which humans represent numbers. We have limited our discussion already, for it is merely humans among all known species who have the ability to count and form numbers which we later can perform calculations upon. Many—often very different—number systems have been employed by many—again, very different—cultures and civilizations throughout the ages, and there still exists a wide variety of them even today, in our comparatively global society. In a much more broad sense, a number system is a set of the many ways humans reason about numbers and this is the definition we will use for our discussion in this paper. But what do we mean by this above definition? Well, let us discuss the ways in which we, as humans, reason about numbers. We reason about numbers by talking about them, so we need a way to represent numbers in speech. We reason about numbers by writing about them, so we need a way to represent numbers in writing/text; this representation is known as a notation. Furthermore, when reasoning about numbers, we need some sort of number base, or radix, which is the fundamental number in which all other numbers...

...THE REALNUMBER SYSTEM
The realnumber system evolved over time by expanding the notion of what we mean by the word “number.” At first, “number” meant something you could count, like how many sheep a farmer owns. These are called the natural numbers, or sometimes the counting numbers.
Natural Numbers
or “Counting Numbers”
1, 2, 3, 4, 5, . . .
* The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever.
At some point, the idea of “zero” came to be considered as a number. If the farmer does not have any sheep, then the number of sheep that the farmer owns is zero. We call the set of natural numbers plus the number zero the whole numbers.
Whole Numbers
Natural Numbers together with “zero”
0, 1, 2, 3, 4, 5, . . .
About the Number ZeroWhat is zero? Is it a number? How can the number of nothing be a number? Is zero nothing, or is it something?Well, before this starts to sound like a Zen koan, let’s look at how we use the numeral “0.” Arab and Indian scholars were the first to use zero to develop the place-value number system that we use today. When we write a number, we use only...

...Polynomial
The graph of a polynomial function of degree 3
In mathematics, polynomials are the simplest class of mathematical expressions (apart from the numbers and expressions representing numbers). A polynomial is an expression constructed from variables (also called indeterminates) and constants (usually numbers, but not always), using only the operations of addition, subtraction, multiplication, and non-negative integer exponents (which are abbreviations for several multiplications by the same value). However, the division by a constant is allowed, because the multiplicative inverse of a non-zero constant is also a constant. For example, x2 − x/4 + 7 is a polynomial, but x2 − 4/x + 7x3/2 is an algebraic expression that is not a polynomial, because its second term involves a division by the variable x (the term 4/x), and also because its third term contains an exponent that is not a non-negative integer (3/2).
A polynomial function is a function which is defined by a polynomial. Sometimes, the term polynomial is reserved for the polynomials that are explicitly written as a sum (or difference) of terms involving only multiplications and exponentiation by non negative integer exponents. In this context, the other polynomials are called polynomial expressions. For example, is a polynomial expression that represents the same thing as the polynomial The term "polynomial", as an adjective, can also be used for quantities that can...