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SCIENTIFIC NOTATION – Notes (STUDENT) Name: __________________ REVIEW: 8³ * 8¯⁶ = __________ 7⁹ ÷ 7¯² = ___________ (4³)² = __________ (6¯³)⁴ = ______________ Standard Form – a number written in its _____________ form. (The ____________ you get when you solve a problem.) Scientific Notation is a way to abbreviate very __________________ or very _________________ using powers of ____. **First number is less than 10, but greater than or = to 1, and second number is a power of _______. WHAT ARE WE DOING??? RULES 1. if + exponent, move the decimal to make the 1st number ___________. Scientific Notation to Standard Form Standard Form to Scientific Notation 2. if a – exponent, move the decimal to make the 1st number ___________. DECIMALS with ZEROS in front (numbers less than 1 whole) = negative exponents 1. Move the decimal point shown until you get BEHIND the first non-zero digit. (This makes a new decimal, *less than 10, and ≥ 1.) 2. Now count how many places the decimal point was moved. (Put that as your negative exponent as a power of 10) WHOLE #’s & Decimals ≥ 1 = positive exponents 1. For Whole #s, place a decimal BEHIND the number and move the decimal until only 1 nonzero digit is in front of the decimal. 2. For Decimals ≥ 1, just move the decimal shown until only 1 digit is in front of the decimal. 3. Now count how many times you moved your decimal. (put that as your + exponent of 10) EXAMPLE PRACTICE 3.12 x 10⁶ 4.17 x 10⁴ 1.35 x 10¯⁴ 3.9 x 10¯³ 0.000057 0.00000045 0.0000003 0.0004 307,000 0.000457 460,100,000 0.0000789 6,980,000 6,500,000 I. Practice: Put the following in Standard Notation: (Remember, + exp., # gets bigger, - exp., # gets smaller) a) 3.12 x 109 f) 8.2 x 106 b) 4.275 x 102 g) 8.2 x 10 c) 1.35 x 10 -6 h) 4.49 x 105 -4 d) 4.7 x 107 i) 7.4 x 101 e) 2.395 x 10 j) 2.6 x 102 -3 k) 7.113 x 10 -3 II. Write in Scientific Notation: (Remember, if # in standard form is < 1, we use – exp., if # > 1, we use + exp.) a) 345,000 b) 62,000,000,000 c) 1,000,000 e) 0.00004 f) 0.000000086 g) 0.25 *d) 345.25 h) 42,050 i) .0005 III. Put the following in Standard Form: a) 6.23 x 104 b) 1.99 x 10 e) 3.114 x 107 f) 2.4 x 10 -4 c) 1.5 x 10 -1 -3 d) 7.5 x 104 g) 1.4 x 1011 h) 6.2 x 10 -8 IV. Put the following in Scientific Notation: a) 59, 740,000 f) 0.000000037 b) 2,300 g) 10,000,000 c) 0.000068 h) 41, 351 d) 0.004 e) 36 i) 0.569 SCIENTIFIC NOTATION – Notes (TEACHER) REVIEW: 8³ * 8¯⁶ = __________ 7⁹ ÷ 7¯² = ___________ Name: ________________ (4³)² = __________ (6¯³)⁴ = ______________ Standard Form – a number written in its original form. (The answer you get when you solve a problem.) Scientific Notation is a way to abbreviate very large numbers or very small numbers using powers of 10. **First number is less than 10, but greater than or = to 1, and second number is a power of __10_____. RULES 1. if + exponent, move the decimal to make the 1st number _BIGGER__. Scientific Notation to Standard Form Standard Form to Scientific Notation 2. if a – exponent, move the decimal to make the 1st number _SMALLER__. DECIMALS with ZEROS in front (numbers less than 1 whole) = negative exponents 1. Move the decimal point until you get BEHIND the first non-zero digit. (This makes a new decimal, *less than 10, and ≥ 1.) 2. Now count how many places the decimal point was moved. (Put that as your - exponent as a power of 10) WHOLE #’s & Decimals ≥ 1 = positive exponents 1. For Whole #s, place a decimal BEHIND the number and move the decimal until only 1 nonzero digit is in front of the decimal. 2. For Decimals ≥ 1, just move the decimal shown until only 1 digit is in front of the decimal. 3. Now count how many times you moved your decimal. (put that as your + exponent of 10) EXAMPLE 3.12 x 10⁶ 3,120,000 PRACTICE 4.17 x 10⁴ 41,700 1.35 x 10¯⁴ 0.000135 3.9 x 10¯³ 0.0039 0.000057 5.7 x 10¯⁵ 0.00000045 4.5 x 10¯⁷ 0.0000003 3.0 x 10¯⁷ 0.0004 4.0 x 10¯⁴ 307,000 3.07 x 10⁵ 0.000457 4.57 x 10¯⁴ 460,100,000 4.601 x 10⁸ 0.0000789 7.89 x 10¯⁵ 6,980,000 6.98 x 10⁶ 6,500,000 6.5 x 10⁶ I. Practice: Put the following in Standard Notation: (Remember, + exp., # gets bigger, - exp., # gets smaller) a) 3.12 x 109 a) 3,120,000,000 f) 8.2 x 106 -3 c) 1.35 x 10 d) 4.7 x 107 e) 2.395 x 10 b) 427.5 c) .000135 d) 47,000,000 e) 0.002395 g) 8.2 x 10 f) 8,200,000 -4 b) 4.275 x 102 -6 h) 4.49 x 105 i) 7.4 x 101 h) 449,000 i) 74 g) .0000082 j) 2.6 x 102 k) 7.113 x 10 j) 260 -3 k) 0.007113 II. Write in Scientific Notation: (Remember, if # in standard form is < 1, we use – exp., if # > 1, we use + exp.) a) 345,000 b) 62,000,000,000 a.) 3.45 x 106 e) 0.00004 e) 4 x 10 b) 6.2 x 1010 f) 8.6 x 10 *d) 345.25 c) 1 x 106 f) 0.000000086 -5 c) 1,000,000 d) 3.4525 x 102 g) 0.25 -8 h) 42,050 g) 2.5 x 10 -1 i) .0005 h) 4.205 x 104 i) 5 x 10 -4 III. Put the following in Standard Form: a) 6.23 x 104 a) 62,300 e) 3.114 x 107 e) 31, 140,000 b) 1.99 x 10 -4 c) 1.5 x 10 b) 0.000199 f) 2.4 x 10 -1 f) 0.24 -3 d) 7.5 x 104 c) 0.0015 d) 75,000 g) 1.4 x 1011 h) 6.2 x 10 g) 140,000,000,000 -8 h) 0.000000062 IV. Put the following in Scientific Notation: a) 59, 740,000 a) 5.974 x 107 f) 0.000000037 f) 3.7 x 10 -8 b) 2,300 b) 2.3 x 103 g) 10,000,000 g) 1 x 107 c) 0.000068 d) 0.004 c) 6.8 x 10 -5 d) 4 x 10 h) 41, 351 h) 4.1351 x 104 e) 36 -3 e) 3.6 x 101 i) 0.569 i) 5.69 x 10 -1