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Name MCA Review – Scientific Notation Scientific Notation: a way to represent very large or very small numbers if it has the form c × 10n where c is A number is written in greater than or equal to and less than and n is a number. Standard form 2,860,000 Product form 2.86 × 1,000,000 Scientific notation 2.86 × 106 110,000 ( decimal places) 1.1 × 1 ( zeros) 1.1 × 10 ? (Exponent is ) To Change from Standard Form to Scientific Notation: 1. Place decimal point such that there is one non-zero digit to the left of the . 2. Count number of decimal places the decimal has " " from the original number. This will be the exponent of the 10. 3. If the original number was less than 1, the exponent is ; if the original number was greater than 1, the exponent is . Examples: Given: 4,750,000 Use: 4.75 (moved Given: 0.000789 decimal places) answer: 7.89 (moved decimal places) answer: You try: Change these numbers from standard form to scientific notation: 1. 61,500 2. 0.0000568 3. 10,000,000,000 To Change from Scientific Notation to Standard Form: 1. Move decimal point to for positive exponent of 10. 2. Move decimal point to for negative exponent of 10. Examples: Given: 1.015 x 10-8 Given: 5.024 x 103 answer: 0.00000001015 answer: 5,024 ( places to ) ( places to ) You try: Change these numbers from scientific notation to standard form: 1. 6 x 107 2. 4.22715 x 108 3. 3.078 x 10-4 Comparing Numbers in Scientific Notation: 1. Compare the is the . The number with the greater the number. 2. If the exponents are the same, then compare the parts. Example: 1.06 x 1016 or 2.4 x 1015 5.28 x 1012 or 5.3 x 1012 You try: Copy and complete the statement using <, >, or =. 1. 9.74 x 1021 2.1 x 1022 2. 4.4 x 107 44,000,000 Greatest Common Factor (GCF) : Numbers that go into a larger number GCF: The greatest common of two or more numbers. 2 ways to find GCF: 1. List all the factors 2. Prime Factorization (use a numbers they have in common) , then multiply only the prime Making a list to find GCF: Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 GCF of 48, 24, 36 is . Prime Factorization to find GCF: 180 10 2 2 18 5 5 126 2 2 2 9 3 63 2 3 3 2 3 21 3 7 2×2×3×3×5 2×3×3×7 GCF of 180 & 126 is . Least Common Multiple (LCM) : the product of the number by any nonzero whole number LCM: The least common of two or more numbers. 2 ways to find LCM: 1. List all the multiples 2. Prime Factorization (use a , then multiply only the prime numbers they have in common once, and then multiply all other numbers as well) Making a list to find the LCM Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, … Multiples of 6: 6, 12, 18, 24, 30, 36, … LCM of 4 & 6: Using Prime Factorization to find the LCM 180 10 2 2 18 5 5 126 2 2 2 9 3 63 2 3 3 2 3 2×2×3×3×5 2×3×3×7 LCM of 180 & 126 is . You try: Find the GCF by listing the factors or using prime factorization: 1. 24, 63 2. 84, 216 Find the LCM by listing the multiples or using prime factorization: 1. 9, 24 2. 28, 46 21 3 7