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 form7x7x7 is standard form

Exponents

• Practice problemsWrite in standard form1) 45=4x4x4x4x4 2) 33=3x3x33) 102=10x10 4)78=7x7x7x7x7x7x7x75) 84=8x8x8x8 6) 96=9x9x9x9x9x97) 27=2x2x2x2x2x2x2

8)69=6x6x6x6x6x6x6x6x6

Exponents

• Write in Exponential form1) 2x2x2x2x2=25 6)

3x3x3x3x3x3x3x3x3=39

2)7x7x7x7=74 7) 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 10greater than 1 but less than 10

Scientific Notation

• Writing from standard form to scientific notation

• Write 3,456,000 in scientific notation1. Find where the decimal starts. 3,456,000.2.Move the decimal to the left between

the first and second numbers.3.456000

3. Drop the zeros3.456

4.Multiple it by power of 103.456x10x fill in the x with the number of places that the decimal was moved3.456x106

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 numbers5.4 x 10x

fill the x in with the number of places that the decimal was moved5.4x10-3 *note* it is a negative 3 now

Scientific Notation

• Write these numbers into scientific notation1) 23000=2.3x104 6) 89600000=8.96x107

2) 0.000045=4.5x10-5 7) 0.0078=7.8x10-3

3) 450=4.5x102 8) 90000=9.0x104

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

5) 79000000=7.9x107 10) 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 right59000.

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=689002) 4.34x10-3=0.00434 7) 2.67x10-5=0.00002673) 5.55x106=5,550,000 8) 3.56x107=356000004) 1.23x10-4=0.000123 9) 7.64x10-

8=0.00000007645) 9.99x109=9,990,000,000 10) 3.43x10-2=0.0343

Order of Operations

• PEMDAS1. Parentheses ()2. Exponent 2x

3. Multiply X4. Divide /5. Add +6. Subtract -

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

Example:9+(12-10)1. Parentheses (12-10) =22. 9+2=113. 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)/111. Parentheses (42+6)

Follow the PEMDAS for what is inside the parenthesis42=4x4=16 insert that into the parentheses(16+6)=22

2. 22/11=2Answer is 2

Order of Operations

Evaluate (solve) each expression

Show all work1) 10+6x26x2=1210+12=22

2)42-3x10+2-3x10=-3042-(-30)=7272+2=74

3)(15-6)x2+20

4)7x8+(2x4)/22

2x4=822=2x2=47x8=5656+8/48/4=256+2=58

5)(52+32+2)/65x5+3x3+2=25+9+2=3636/6=6

A number is divisible by… Rules of Divisibility

2 If the number is even

3 If the sum of the digits is divisible by 3

4 If the last two digits in a number are divisible by 4

5 If the number ends in 0 or 5

6 If the number is divisible by both 2 AND 3

9 If the sum of the digits in a number is also divisible by 9

10 If the number end in 0

Divisibility

Rules of Divisibility• Using the rules of divisibility determine whether each

number is divisible by 2,3,4,5,6,9,and 101)90 5) 1442,3,5,6,9,10 2,3,4,6,92)308 6) 2282,4 2,3,4,63)435 7)6343,5 2 4)402 8)1112,3,6 3

Prime and Composite numbers

• PrimeA prime number is a

number that is ONLY divisible by 1 and itself

Example 13The only factors that 13 is

divisible by is 1 & 1313/1=13 or 13/13=1

• CompositeA composite number is a number

that is divisible by more than two factors.

Example: 2424 is divisible by

1,2,3,4,6,8,12,24There are more factors that 24 is

divisible b y other than 1 and itself.

24/2=12 24/12=224/3=8 24/8=3 etc.

Prime & Composite

• Tell whether each number is prime or composite1) 4 Composite 6) 16 Composite2) 13 Prime 7) 52 Composite3) 45 Composite 8) 11 Prime4) 33 Composite 9) 41 Prime5) 99 Composite 10) 58 Composite

Prime Factorization

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

2x3=62 & 3 are factor of the

product 6List all the factors of 181,2,3,6,9,18

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 numbers24 4 6 2 2 2 3 24=2x2x2x3

Prime Factorization

• List all the Factors1) 6 2) 212,3,6 3,7,213) 20 4) 362,4,5,10,20 2,3,4,6,9

Prime FactorizationWrite the Prime Factorization of each number1)36 4)54 6 x 6 9x62 x3 2x3 3x3 2x336=2x2x3x3 or 22x32 54=2x3x3x3 or 2x33

2)18 5) 45 9x2 5x93x3 3x3 18=2x3x3 or 2x32 45=3x3x5 or 32x5

3)72 6) 64 9x8 8x83x3 4x2 2x4 2x4 2x2 2x2 2x272=2x2x2x3x3 or 23x32 64=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 241,2,3,4,6,8,12,24The factors of 321,2,4,8,16,328 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 multiplesExample: what is the LCM of

6 & 9Multiples of 66,12,18,24,30Multiples of 99,18,27,3618 is the least common multiple.

GCF & LCM Examples

• Find the GCF1)12 & 15 5)16, 28, &482)18&25 6)20, 30, 803)15&25 7)15, 35,&954)36&45 8) 25, 75, & 115Find the LCM1)3,6,& 9 4)3,5,& 92)10, 15 5)4,7, &143)3,9,12 6)8, 12

GCF answer• Find the GCF1)12 & 15 5)16, 28, &4812:2,3,4,6,12 16:2,4,8,1615:3,5 28:2,4,7,14,28 48: 2,3,4,6,8,12,16,24,482)18&25 6)20, 30, 8018:2,3,6,9 20:2,4,5,10,2025:5,25 30:2,3,5,6,10,30No GCF 80:2,4,5,8,10,16,20,40,80

3)15&25 7)15, 35,&9515:3,5,15 15:3,5,1525:5,25 35: 5,7,35

95: 5,19,954)36&45 8) 25, 75, & 11536:2,3,4,6,9 25:5,25 45:3,5,9,15,45 75:3,5,15,25,75 115:5,23,115

LCM AnswersFind the LCM1)3,6,& 9 4)3,5,& 93:3,6,9,12,15,18 3:3,6,9,12,15,18,21,24,27,30,33,36,39,42,456:6,12,18 5:5,10,15,20,25,30,35,40,459:9,18 9:9,18,27,36,452)10, 15 5)4,7, &1410:10,20,30 4:4,8,12,16,20,24,2815:15,30 7:7,14,21,28,35

14:14,283)3,9,12 6)8, 123:3,6,9,12,15,18,21,24,27,30,33,36 8:8,16,249:9,18,27,36,45 12:12,24,3612:12,24,36