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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation3.1 Type of Numbers: Natural, Whole, Integers, Rational, Irrational & Real

Natural Numbers(N):
Natural Numbers are counting numbers from 1,2,3,4,5,................
N = {1,2,3,4,5,................}

Whole Numbers (W):
Whole numbers are natural numbers including zero. They are 0,1,2,3,4,5,...............
W = {0,1,2,3,4,5,..............}
W = 0 + N

Positive Numbers:
Positive numbers are, 1,2 ,3 ,4 ,5.................
Positive Numbers: {1, 2, 3, . . .}

Negative Numbers:
Negative numbers are, ............-3, -2, -1.
Negative integers: { . . . -3, -2, -1}

Integers (Z):

• Whole Numbers together with negative numbers.
• Integers are set containing the positive numbers, 1, 2, 3, 4, ...., and negative numbers,............-3, -2, -1, together with zero.
• Zero is neither positive nor negative, but is both.
• In other words, Integers are defined as set of whole numbers and their opposites.
• Z = {..., -3, -2, -1, 0, 1, 2, 3, .....}

Rational Numbers (Q):

• All numbers of the form , where a and b are integers (but b cannot be zero)
• Rational numbers include fractions:
* Proper Fraction: Numbers smaller than 1 eg: 1/2 or 3/4
* Improper Fraction: Numbers greater than 1 eg: 5/2
* Mixed Fraction: 2 1/2 = 5/2
• Powers and square roots may be rational numbers if their standard form is a rational number.
• In rational numbers the denominator cannot be zero
Example:
2 can be expressed in the form of p/q as 2/1
-13/9 = -1.444.......
8-2 = 0.015625
(Ö16)/3 = 4/3 = ±1.333...
Ö4 = 2 1/2 = 0. 5 ----- Rational (terminates)
2/3 = 0.6666666.......Rational (repeats)
5/11 = 0.454545......Rational (repeats)

Irrational Numbers Q1:

• Cannot be expressed as a ratio of integers.
• As decimals they never repeat or terminate (rationals always do one or the other)
• They go on for ever or infinity.
Example: Ö2, Ö3, Ö7, Ö8
square root of 2 = Ö2 = 1. 41421356......Irrational (never repeats or terminates)
pi = p = 22/7 = 3.14159265....... Irrational (never repeats or terminates)

Real Numbers R:

• Real Numbers are every number, irrational or rational.
• Any number that you can find on the number line.
• It is a number required to label any point on the number line; or it is a number that names the distance of any point from 0.
• R = Q + Q1
• Natural Numbers are Whole Numbers, which are Integers, which are Rational Numbers, which are Real Numbers.
• Irrational Numbers are Real Numbers, but not all Real Numbers are Irrational Numbers.

Examples:
 0.45 rational real 3.1415926535................... irrational, real 3.14159 rational, real 0 whole, integer, rational, real 5/3 rational, real 1 2/3 = 5/3 rational, real Ö2 = 1. 41421356...... irrational, real -Ö81 = -9 integer, rational, real -9/3 rational, real Ö25 = 5 natural, whole, integer, rational, real 9/3 = 3 natural, whole, integer, rational, real -3/4 rational, real p = 3.1428571... irrational, real 3.144444....... rational, real (since it is a repeating decimal)

Directions: Choose the correct answer. Also, write five examples of your own for each type of number.
 Q 1: Which is NOT a Rational Number?sqrt(2)03.14sqrt(4) Q 2: Which is true?All of the otherAll irrational numbers are real.All whole numbers are real.All rational numbers are real. Q 3: Identify the Irrational Number.3.14105/21pisqrt(81) Q 4: What is N U W? (N -> Natural numbers, W -> Whole numbers, I -> Integers, Q -> Rational numbers)WINQ Q 5: A rational number is also an integer. (Hint: 4/1 is an integer but 2/3 is not.)FalseTrue Q 6: If Q1 is set of irrational numbers. What is Q1intersection of Q?Qnullnone of theseQ1 Q 7: Which of the following is real number?5.9all of these1000square root of 2 Q 8: Ö16rationalnegativeirrational Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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