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Unit 1 study guide math

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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.
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

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

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

- 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 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 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 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 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 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 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

- 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 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 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

- 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
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

- 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

- 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 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 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 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

- 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

- 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

- 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

- 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

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

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