Estimating Square Roots, Rational and Irrational Numbers Vocabulary, The Real Number System, The Real Number System, Repeating Decimals as Fractions, Ordering and Comparing Rational Numbers, Classifying Real Numbers, Classifying numbers, Square Roots...

-2345

Integer, Rational, Real

-30

Integer, Rational, Real

-54/9

Integer, Rational, Real

-93/3

Integer, Rational, Real

1/2

Real, Rational

-12/2

Real, Rational, Integer

0

Real, Rational, Integer, Whole

5

Real, Rational, Integer, Whole, Natural

radical symbol

Square root symbol

Radicand

The expression under the radical sign

Negative Integers

The integers that are less than zero. They are the opposites of the positive integers.

Positive Integers

The positive integers are the numbers used to count. They are the numbers {1, 2, 3, 4, 5,...}. They are also called the counting numbers.

principal square root

The positive square root of a number, indicated by the radical sign

Natural Numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbers.

Integers

The set of whole numbers and their opposites

-2.23, -2 2/5, and -0.95

Which numbers from this list are less than -0.94? -15/16, 0.24, -2.23, 97%, -2 2/5, -0.95

0.1818181818

2/11

0.22222222

2/9

0.2424242424

8/33

repeating decimal

A decimal in which the same block of digits repeats without end.

Perfect Square

A number that can be expressed by multiplying a number times itself (squaring a counting number)

Rational number

A number that can be written as a fraction

Exponent

A number that tells how many times the base should be multiplied by itself

Irrational number

A number whose decimal form is nonterminating and nonrepeating. Irrational numbers can't be expressed as fractions.

Non-Terminating Decimals

A number with a decimal that does not end/stop (3.1415...)

Perfect Square

A number with a square root that is a rational number.

perfect cube

A rational number whose cube root is a whole number.

perfect square

A rational number whose square root is a whole number

Fraction

expressed with a numerator and a denominator, numerator divided by denominator

equivalent

having the same value

Integers

{...-3,-2,-1,0,1,2,3...}

Whole Numbers

{0,1,2,3,4...}

Natural Numbers

{1,2,3,4...}

Between 9 and 10. Closer to 10

√99

0.333333333

1/3

0.111111111

1/9

0.3636363636

4/11

0.44444444

4/9

0.4545454545

5/11

Real numbers

All rational and irrational numbers

Fractions

Consist of two numbers separated by a bar which indicates division: the numerator is above the bar and the denominator is below the bar

12.569843681549...

Irrational & Real

π

Irrational & Real

√15

Irrational & Real

√7

Irrational & Real

0.16, 0.10, 0.07, -1.43, -2.65

List the numbers from greatest to least. 0.10, -2.65, 0.16, -1.43, 0.07

-2.65, -1.43, 0.07, 0.10, 0.16

List the numbers from least to greatest. 0.10, -2.65, 0.16, -1.43, 0.07

Whole Numbers

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

17

Natural, Whole, Integer, Rational Real

42/6

Natural, Whole, Integer, Rational, Real

5

Natural, Whole, Integer, Rational, Real

√81

Natural, Whole, Integer, Rational, Real

√9

Natural, Whole, Integer, Rational, Real

square root

One of the two equal factors of a number

cube root

One of three equal factors of a number.

-0.650 , -3/7 , -2/9 , -0.200

Order from Least to Greatest: -0.650, -3/7, -2/9, -0.200

-3/4 , -1/2 , -1/10

Order from Least to Greatest: -1/2, -3/4, -1/10

-250, -200, -150, 0, 50, 200

Order from Least to Greatest: -150, -200, 50, 0, 200, -250

-7/8 , -0.6 , -0.5 , -4/9 ,-2/5 , -0.35

Order from Least to Greatest: -2/5, -4/9, -0.5, -7/8, -0.35, -0.6

0.1, 0.5, 1.6, 2.3, 3.2

Order from Least to Greatest: 0.5, 2.3, 3.2, 1.6, 0.1

3, 2.91, -0.3, -0.9, -1.01

Order the numbers from greatest to least. -0.3, 3, 2.91, -0.9, -1.01

1/12, 0.08, 1/20, 0.03

Order the numbers from greatest to least. 0.08, 1/12, 0.03, 1/20

-1.01, -0.9, -0.3, 2.91, 3

Order the numbers from least to greatest. -0.3, 3, 2.91, -0.9, -1.01

84/9, 7.25, 46/7, 6 1/4, -5.58, -6 1/2

Order these numbers from greatest to least. -6 1/2, 7.25, 46/7, 6 1/4, -5.58, 84/9

-6 1/2, -5.58, 6 1/4, 46/7, 7.25, 84/9

Order these numbers from least to greatest. -6 1/2, 7.25, 46/7, 6 1/4, -5.58, 84/9

-2/3

Rational & Real

-43.76

Rational & Real

0.333...

Rational & Real

23.9

Rational & Real

32.343434343...

Rational & Real

Each number is greater than 0.5.

Which statement is true about the following numbers: 0.4, 20/100, 4/9, 0.04? Each number is less than 0.5. OR Each number is greater than 0.65.

Each number is greater than 0.5.

Which statement is true about the following numbers: 0.8, 60/100, 5/9, 0.57? Each number is less than 0.65. OR Each number is greater than 0.5.

0

Whole, Integer, Rational, Real

repeating decimal

a decimal number that has digits that repeat forever

repeating decimal

a decimal that does not have a definite end to it (The place value of the last digit in the number cannot be found.)

non-repeating decimal

a decimal that does not have digits that repeat forever

Terminating Decimal

a decimal that ends, or terminates

non-terminating decimal

a decimal that goes on forever and ever

terminating decimal

a decimal that has a definite end to it (The place value of the last digit in the number can be found.)

Non-terminating Decimal

a decimal that is continuous and never ends

Irrational Numbers

a decimal that never ends and never repeats

Repeating Decimal

a decimal with a digit(s) that repeat in a pattern

Base

a number raised to an exponent

rational number

a number that can be made by dividing two integers

Rational Number

a number that can be written as a fraction

irrational number

a number that cannot be expressed as a terminating decimal, repeating decimal, or as a fractional equivalent

Non-perfect Square

a number that cannot be expressed by multiplying a number times itself

irrational number

a number that cannot be written as a ratio of integers

Non-Perfect square

a number that does not have a whole-number square root. irrational number

Square Root

a number that produces a specified quantity when multiplied by itself

perfect square

a number that result from multiplying an integer by itself

Square Root

a number that when multiplied by itself equals a given number

square root

a number that when multiplied to itself results in a specified number. The square root of 25 is 5, since 5x5=25 (25 is the specified number)

real number

all rational and irrational numbers

standard notation

an answer or value

"squared"

an exponent of 2

"cubed"

an exponent of 3

Positive Integers

any integer greater than zero

Negative Integers

any integer less than zero

Natural Numbers

counting numbers

Whole Numbers

counting numbers and zero

terminating decimal

decimal number that has digits that do not go on forever

Terminating Decimals

decimals that end.

square root

the inverse of an exponent of 2, symbol is √

power

the name for a base with an exponent

Real Number

the set of rational and irrational numbers

radical

the symbol for a square root, look like this: √

notation

the way something is written

estimate

to find a value that is close enough to the right answer, usually with some thought or calculation involved

Integers

whole numbers and their opposites

expanded notation

written as repeated multiplication

exponential notation

written with a base and an exponent

Between 3 and 4. Closer to 3

√10

10

√100

10.5

√110

3.5

√12

11

√121

Between 11 and 12. Closer to 11

√125

3.7

√14

Between 11 and 12. Closer to 12

√140

12

√144

12.1

√145

Between 3 and 4. Closer to 4

√15

12.2

√150

Between 12 and 13. Closer to 12

√150

4

√16

Between 12 and 13. Closer to 13

√165

13

√169

4.2

√18

Between 4 and 5. Closer to 4

√18

4.4

√19

13.9

√195

14

√196

Between 1 and 2. Closer to 1

√2

Between 14 and 15. Closer to 14

√200

14.8

√220

Between 14 and 15. Closer to 15

√220

15

√225

Between 4 and 5. Closer to 5

√24

5

√25

16

√256

Between 5 and 6. Closer to 5

√27

17

√289

5.4

√29

17.1

√290

Between 1 and 2. Closer to 2

√3

18

√324

18.2

√333

5.8

√34

Between 5 and 6. Closer to 6

√35

6

√36

19

√361

19.4

√376

Between 6 and 7. Closer to 6

√38

20

√400

6.4

√41

6.8

√46

Between 6 and 7. Closer to 7

√48

7

√49

Between 2 and 3. Closer to 2

√5

Between 7 and 8. Closer to 7

√50

Between 7 and 8. Closer to 8

√60

8

√64

Between 8 and 9. Closer to 8

√65

8.2

√67

8.7

√75

Between 2 and 3. Closer to 3

√8

Between 8 and 9. Closer to 9

√80

9

√81

Between 9 and 10. Closer to 9

√85

3

√9