140 terms

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)

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.

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!

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