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Real Number System
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Terms in this set (140)
irrational
Numbers that can't be written as a fraction. Includes decimals that don't end or repeat
rational
Numbers that can be written as a fraction. Includes decimals that end or repeat
integers
Positive and negative whole numbers and zero
whole
Only positive whole numbers and zero
Irrational
√3
Rational, integer, whole
25/5
Rational
-2.6
Rational, integer, whole
0
Rational, integer
-13
Rational, integer, whole
√49
Rational
2/3
Rational, integer
-√4
Rational
3/5
Irrational
√17
Irrational
π
Natural numbers
1, 2, 3, 4, 5,....
Sometimes called "counting numbers" (Think of your fingers)
Whole numbers
0, 1, 2, 3, 4, 5,...
Remember "whole" has what looks like a "zero" in the middle of the word.
Integers
...-4, -3, -2, -1, 0, 1, 2, 3, 4...
All positive and negative numbers, plus the zero
BUT NO FRACTIONS OR DECIMALS!
Ratonal numbers
Any number that can be written as a fraction (a/b) where b is not zero. This includes all terminating or repeating decimal numbers.
Irrational numbers
Any number that CAN NOT be written as a fraction (non-terminating, non-repeating decimal numbers).
Real numbers
The set of all rational and irrational numbers
π, √2, √5,√10
Irrational numbers, real numbers
0, 1/2, 52.324, 32, 3¾
Rational numbers, real numbers
-46, -30, 167, 3,208
Integers, rational numbers, real numbers
1, 39, 42, 608
natural numbers, whole numbers, integers, rational numbers and real numbers.
additive identity
the sum of any number and zero will equal the same number
additive inverse
the opposite of a number that will make a sum of zero
associative property
changing the grouping does not change their sum or product; (a+b)+c= a+(b+c)
commutative property
changing the order of the numbers does not change their sum or product; a+b= b+a
distributive property
terms in an expression can be expanded to form an equivalent expression; a (b+c)= ab + ac
identity
an equation that is true no matter what values are chosen
identity element
a number that will not change the original number
integers
all whole numbers (both positive and negative) and zero
inverse
operations that undo each other
irrational numbers
numbers that can not be expressed as a ratio or fraction
multiplicative property of zero
product of any number and zero is zero (a x 0=0)
multiplicative identity
any number times one equals that number (Nx1=N)
natural numbers
all positive integers (not including zero)
real numbers
the set of numbers that includes rational and irrational numbers
reciprocal
the inverse of the numerator and denominator in a fraction; when multiplied by the original fraction, it results in a product that equals one
rational numbers
numbers that can be expressed as a ratio or fraction
whole numbers
all positive integers (including zero)
Natural numbers
Counting numbers
Whole numbers
Counting numbers and zero
Integers
Whole numbers and their opposites
Rational numbers
Any number that can be expressed as a ratio of two integers
Irrational numbers
Nonrepeating, nonterminating decimals
True or False: All rational numbers are real numbers.
True
True or False: All whole numbers are integers.
True
True or False: All integers are whole numbers.
False
True or False: Zero is an irrational number.
False
True or False: The number .262662666266662... is a rational number.
False
Commutative Property of Addition
a+b=b+a
Commutative Property of Multiplication
a x b=b x a
Associative Property of Addition
(a+b)+c=a+(b+c)
Associative Property of Multiplication
(a x b) x c= a x (b x c)
Distributive Property
a(b+c)=ab+ac / a(b-c)=ab-ac
Additive Identity Property
a+0=a
Multiplicative Identity Property
a x 1=a
Additive Inverse Property
a+-a=0
Multiplicative Inverse Property
a x 1/a=1
The Closure Property
A set of numbers is closed (under an operation) if and only if the operation on two of the numbers of the set produces another number of the set. If a number outside the set is produced, then the set is not closed.
Real Number
The set of rational numbers and the set of irrational numbers
Imaginary Numbers
A number that when squared it gives a negitive result
Rational Number
Numbers that can be written as a fraction
Integers
Negitive and positive natural numbers
Whole Numbers
Numbers from 0 and up
Natural Numbers
Numbers from 1 and up. NO ZERO
Terminating Decimal
A decimal that ends
Repeating Decimal
A decimal in which a pattern of one or more digits is repeated indefinitely
Period
The series of numbers that repeat in a repeating decimal
Bar Notation
A line that is used in a repeating decimal to indicate the digits that repeat
Irrational Numbers
Numbers that cannot be expressed as a terminating or repeating decimal
Perfect Square
A number whose square root is a rational number
Principal Square Root
the non-negitive square root of a number. Radical:a square root sign
Radicand
the expression that is under the radical sign
The negitive square root of 64
Rational, Integer
The square root of 28
Irrational
The square root of 10.24
Rational
-54 over 19
Rational
Simplify: The Square root of 36 over 81
2/3
Product property
Square root of 400. Square root of 4
100. square root of 4
the square rooot of 100
Quotient Property
The square root of 1/2. The Squaure root of 1 / The square root of 2
The Square root of 200
10Squareroot2
The Square root of 3/4
square rooot of 3 / 2
The Square root of 20/4
Square root of 5/2
The square root of 32/50
4/5
5 square root 2* The square root of 2
10
3 Square root of 63* the square root of 4
18 square root 7
1/2 Square root of 112
2 square root 7
8 square root 13/19
8 square root 15/3
The square root of 10* the square root of 16/the square root of 5
-2the square root of 5/5
the square root of 48
4 the square root of 3
a=3 b=4 c=?
5=C
√5
irrational
2.3987432...
irrational
½
rational
-|-9|
rational
-√16
rational
7/9
rational
pi
irrational
-√2
irrational
¾
rational
0.8976321...
irrational
-9.876.....
irrational
|5| - 3
rational
1.8
rational
3²
rational
√12
irrational
(-3)³
rational
|√7|
irrational
4.3
rational
8.6
rational
12.14
rational
2/3
rational
8/5
rational
14÷3
rational
-|9.1|
rational
3.4
rational
1.888...
rational
1/4
rational
√40
irrational
√36
rational
4.72384...
irrational
-3
rational
-0.165
rational
-13.2894...
irrational
3.14... (pi)
irrational
real number
number set that includes rational and irrational numbers
irrational number
number set that includes numbers that cannot be expressed as a fractions; non terminating decimals
rational number
number set including all numbers that can be written as a fraction where the denoninator is not equal to zero
integer
all the whole numbers, including zero and their negatives
whole number
zero and all the counting numbers from 1 and on
counting number
all the whole numbers from 1 and on - does not include zero
natural number
also called counting numbers - include all whole numbers from 1 on
terminating decimal
a decimal that ends; type of rational number
non terminating decimal
a decimal the never ends and goes on forever; type of irrational number
repeating decimal
decimal in which a number or group of numbers continues to repeat. represented as a bar over the repeating numbers
non-repeating decimal
a decimal that doesn't end or repeat. Type of irrational number
Pi
example of an irraational number because it cannot be expressed as a fraction, a terminating decimal or repeating decimal
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