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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. 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

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  1. Unit 1 study guide math Exponents, Scientific Notation, Order of Operation, Greatest Common Factor, Least Common Multiple

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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.

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. Divisibility

  16. 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

  17. 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.

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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.

  25. 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

  26. 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

  27. 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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