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Unit 1 study guide math. Exponents, Scientific Notation, Order of Operation, Greatest Common Factor, Least Common Multiple. Exponents. What is an Exponent? What is Exponential form?. An Exponent tells how many times a number is multiplied by itself. 7 3 = 7X7X7= 343

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Unit 1 study guide math

Unit 1 study guide math

Exponents, Scientific Notation, Order of Operation, Greatest Common Factor, Least Common Multiple


Exponents
Exponents

  • What is an Exponent?

  • What is Exponential form?

  • An Exponent tells how many times a number is multiplied by itself.

    73= 7X7X7= 343

  • A number is written in exponential form when the number is written with an exponent.

    73 is exponential form

    7x7x7 is standard form


Exponents1
Exponents

  • Practice problems

    Write in standard form

  • 45=4x4x4x4x42) 33=3x3x3

  • 102=10x104)78=7x7x7x7x7x7x7x7

    5) 84=8x8x8x8 6) 96=9x9x9x9x9x9

    7) 27=2x2x2x2x2x2x2 8)69=6x6x6x6x6x6x6x6x6


Exponents2
Exponents

  • Write in Exponential form

    1) 2x2x2x2x2=25 6) 3x3x3x3x3x3x3x3x3=39

    2)7x7x7x7=747) 4x4x4x4x4x4=46

    3)9x9x9=93 8) 8x8x8x8x8=85

    4)6x6x6x6x6x6x6x6=68 9) 12x12=122

    5)5x5=52 10) 11x11x11=113


Scientific notation
Scientific Notation

  • What is Scientific Notation?

  • Scientific notation is used to express very large or very small numbers.

  • A number written in scientific notation has two parts that are multiplied.

    1.2345 x 104

    The first part is a number 2nd is a power of 10

    greater than 1 but less than 10


Scientific notation1
Scientific Notation

  • Writing from standard form to scientific notation

  • Write 3,456,000 in scientific notation

  • Find where the decimal starts.

    3,456,000.

    2.Move the decimal to the left between the first and second numbers.

    3.456000

  • Drop the zeros

    3.456

    4.Multiple it by power of 10

    3.456x10x fill in the x with the number of places that the decimal was moved

    3.456x106


Scientific notation2
Scientific Notation

  • If the number starts out large like 3,456,000 then the power of 10 in the scientific notation will have a positive exponent.

  • If the number starts out small like 0.0054 then the power of 10 in scientific notation will have a negative exponent.

  • Example: 0.0054 find the decimal and move it to the right between the first two non zero numbers

    5.4 x 10x

    fill the x in with the number of places that the decimal was moved

    5.4x10-3 *note* it is a negative 3 now


Scientific notation3
Scientific Notation

  • Write these numbers into scientific notation

    1) 23000=2.3x1046) 89600000=8.96x107

    2) 0.000045=4.5x10-57) 0.0078=7.8x10-3

    3) 450=4.5x1028) 90000=9.0x104

    4) 0.00098=9.8x10-4 9) 0.023=2.3x10-2

    5) 79000000=7.9x10710) 0.000008=8.0x10-6


Scientific notation4
Scientific Notation

  • How do you change Scientific Notation into Standard form?

  • When given a number already in scientific notation look at the exponent with the power of 10.

    5.9 x 104

    The exponent with the power of 10 is a positive 4

    That means the decimal is going to move 4 places to the right

    59000.


Scientific notation5
Scientific Notation

  • How do you change Scientific Notation into Standard form?

  • When given a number already in scientific notation look at the exponent with the power of 10.

    8.7x10-5

    The exponent with the power of 10 is a negative 5

    That means the decimal is going to move 5 places to the left

    .000087


Scientific notation6
Scientific Notation

  • Change the following from Scientific notation to Standard form.

    1) 8.0x102=800 6) 6.89x104=68900

    2) 4.34x10-3=0.004347) 2.67x10-5=0.0000267

    3) 5.55x106=5,550,0008) 3.56x107=35600000

  • 1.23x10-4=0.0001239) 7.64x10-8=0.0000000764

    5) 9.99x109=9,990,000,000 10) 3.43x10-2=0.0343


Order of operations
Order of Operations

  • PEMDAS

  • Parentheses ()

  • Exponent 2x

  • Multiply X

  • Divide /

  • Add +

  • Subtract -

  • When solving a multi-step use the order of operation to solve for the correct answer.

    Example:

    9+(12-10)

  • Parentheses (12-10) =2

  • 9+2=11

  • 9+(12-10)=2


Order of operations1
Order of Operations

  • PEMDAS

  • **note**

  • Multiplication doesn’t always come before division it was ever comes first when reading from left to right .

  • Addition doesn’t always come before subtraction its whatever comes first when reading from left to right.

  • Examples:

    (42+6)/11

  • Parentheses (42+6)

    Follow the PEMDAS for what is inside the parenthesis

    42=4x4=16 insert that into the parentheses

    (16+6)=22

  • 22/11=2

    Answer is 2


Order of operations2
Order of Operations

Evaluate (solve) each expression

Show all work

  • 10+6x2

    6x2=12

    10+12=22

    2)42-3x10+2

    -3x10=-30

    42-(-30)=72

    72+2=74

    3)(15-6)x2+20

4)7x8+(2x4)/22

2x4=8

22=2x2=4

7x8=56

56+8/4

8/4=2

56+2=58

5)(52+32+2)/6

5x5+3x3+2=25+9+2=36

36/6=6



Rules of divisibility
Rules of Divisibility

  • Using the rules of divisibility determine whether each number is divisible by 2,3,4,5,6,9,and 10

    1)90 5) 144

    2,3,5,6,9,10 2,3,4,6,9

    2)308 6) 228

    2,4 2,3,4,6

    3)435 7)634

    3,5 2

    4)402 8)111

    2,3,6 3


Prime and composite numbers
Prime and Composite numbers

  • Prime

    A prime number is a number that is ONLY divisible by 1 and itself

    Example 13

    The only factors that 13 is divisible by is 1 & 13

    13/1=13 or 13/13=1

  • Composite

    A composite number is a number that is divisible by more than two factors.

    Example: 24

    24 is divisible by 1,2,3,4,6,8,12,24

    There are more factors that 24 is divisible b y other than 1 and itself.

    24/2=12 24/12=2

    24/3=8 24/8=3 etc.


Prime composite
Prime & Composite

  • Tell whether each number is prime or composite

  • 4 Composite 6) 16 Composite

  • 13 Prime 7) 52 Composite

  • 45 Composite8) 11 Prime

  • 33 Composite9) 41 Prime

  • 99 Composite10) 58 Composite


Prime factorization
Prime Factorization

  • What are factors?

  • Factors are whole numbers that are multiplied together to get a product

    2x3=6

    2 & 3 are factor of the product 6

    List all the factors of 18

    1,2,3,6,9,18


Prime factorization1
Prime factorization

  • What is Prime Factorization?

  • The prime factorization of a number is the number written as a product of its primes.

    Example: Prime factorize the number 24 circle the prime numbers

    24

    4 6

    2 2 2 3

    24=2x2x2x3


Prime factorization2
Prime Factorization

  • List all the Factors

  • 6 2) 21

    2,3,6 3,7,21

  • 20 4) 36

    2,4,5,10,20 2,3,4,6,9


Prime factorization3
Prime Factorization

Write the Prime Factorization of each number

1)36 4)54

6 x 6 9x6

2 x3 2x3 3x3 2x3

36=2x2x3x3 or 22x32 54=2x3x3x3 or 2x33

2)18 5) 45

9x2 5x9

3x3 3x3

18=2x3x3 or 2x32 45=3x3x5 or 32x5

3)72 6) 64

9x8 8x8

3x3 4x2 2x4 2x4

2x2 2x22x2

72=2x2x2x3x3 or 23x3264=2x2x2x2x2x2 or 26


Greatest common factor
Greatest Common Factor

  • What is the Greatest Common Factor?

  • The GCF is the largest of the COMMON factors shared by 2 or more whole numbers.

    Example: What is the GCF of

    24 & 32

    The factors of 24

    1,2,3,4,6,8,12,24

    The factors of 32

    1,2,4,8,16,32

    8 is the greatest common factor between 24&32


Least common multiple
Least Common Multiple

  • What is the Least Common Multiple?

  • The LCM is the smallest number that is a multiple of 2 or more numbers.

  • Use a number line to count the multiples

    Or you can list the multiples

    Example: what is the LCM of

    6 & 9

    Multiples of 6

    6,12,18,24,30

    Multiples of 9

    9,18,27,36

    18 is the least common multiple.


Gcf lcm examples
GCF & LCM Examples

  • Find the GCF

    1)12 & 15 5)16, 28, &48

    2)18&25 6)20, 30, 80

    3)15&25 7)15, 35,&95

    4)36&45 8) 25, 75, & 115

    Find the LCM

    1)3,6,& 9 4)3,5,& 9

    2)10, 15 5)4,7, &14

    3)3,9,12 6)8, 12


Gcf answer
GCF answer

  • Find the GCF

    1)12 & 15 5)16, 28, &48

    12:2,3,4,6,12 16:2,4,8,16

    15:3,5 28:2,4,7,14,28

    48: 2,3,4,6,8,12,16,24,48

    2)18&25 6)20, 30, 80

    18:2,3,6,9 20:2,4,5,10,20

    25:5,25 30:2,3,5,6,10,30

    No GCF 80:2,4,5,8,10,16,20,40,80

    3)15&257)15, 35,&95

    15:3,5,15 15:3,5,15

    25:5,25 35: 5,7,35

    95: 5,19,95

    4)36&45 8) 25, 75, & 115

    36:2,3,4,6,9 25:5,25

    45:3,5,9,15,45 75:3,5,15,25,75

    115:5,23,115


Lcm answers
LCM Answers

Find the LCM

1)3,6,& 9 4)3,5,& 9

3:3,6,9,12,15,18 3:3,6,9,12,15,18,21,24,27,30,33,36,39,42,45

6:6,12,18 5:5,10,15,20,25,30,35,40,45

9:9,18 9:9,18,27,36,45

2)10, 15 5)4,7, &14

10:10,20,30 4:4,8,12,16,20,24,28

15:15,30 7:7,14,21,28,35

14:14,28

3)3,9,12 6)8, 12

3:3,6,9,12,15,18,21,24,27,30,33,36 8:8,16,24

9:9,18,27,36,45 12:12,24,36

12:12,24,36