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Scientific Notation

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**Scientific Notation 과학적 기수법**

A short-hand way of writing large numbers without writing all of the zeros.

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**The Distance From the Sun to the Earth in miles**

93,000,000

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**Step 1 93,000,000 = 9.3000000 Move decimal left**

Leave only one number in front of decimal (one number to the left of the decimal). 93,000,000 =

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Step 2 Write number without zeros 93,000,000 = 9.3

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**Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal**

Make that your power of ten 93,000,000 = 9.3 x 10 7

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**The power of ten is 7 because the decimal moved 7 places. 7**

93,000,000 = 9.3 x 10 7

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**93,000,000 --- Standard Form (Decimal form)**

9.3 x Scientific Notation

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**Scientific notation Decimal notation Scientific notation 127**

(정수) Decimal notation Scientific notation 127 1.27 x 102 0.0907 9.07 x 10 – 2 5.06 x 10 – 4 2.3 x 1012

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**Place Value Decimal System**

1 2 3 . 4 5 6 7 Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Ten thousandths Hundred Thousandths Millionths Ten Millionths 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 20 0.4 0.05 0.006 0.0007 `

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**When using Scientific Notation, there are two kinds of exponents: positive and negative**

Positive Exponent: 2.35 x 108 Negative Exponent: 3.97 x 10-7

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When changing scientific notation to standard notation, the exponent tells you if you should move the decimal: With a positive exponent, move the decimal to the right: 4.08 x 103 = 4 0 8 Don’t forget to fill in your zeroes!

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When changing scientific notation to standard notation, the exponent tells you if you should move the decimal: With a negative exponent, move the decimal to the left: 4.08 x 10-3 = Don’t forget to fill in your zeroes!

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**An easy way to remember this is:**

If an exponent is positive, the number gets larger, so move the decimal to the right. If an exponent is negative, the number gets smaller, so move the decimal to the left.

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**The exponent also tells how many spaces to move the decimal:**

In this problem, the exponent is +3, so the decimal moves 3 spaces to the right.

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**The exponent also tells how many spaces to move the decimal:**

In this problem, the exponent is -3, so the decimal moves 3 spaces to the left.

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**When changing from Standard Notation to Scientific Notation:**

1) First, move the decimal after the first whole number: 2) Second, add your multiplication sign and your base (10). x 10 3) Count how many spaces the decimal moved and this is the exponent. x 10 3 3 2 1

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**When changing from Standard Notation to Scientific Notation:**

4) See if the original number is greater than or less than one. If the number is greater than one, the exponent will be positive. = x 105 If the number is less than one, the exponent will be negative. = 6.72 x 10-8

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**Page 82 Try changing these numbers to proper Scientific Notation:**

430 3,400,000 11.2 x 104 0.01 x 10-2 4.3 x 102 3.4 x 106 4.5 x 10-6 1.12 x 105 1 x 10-4

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**Rewrite these in decimal form Page 82**

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**Multiplying with Scientific Notation**

(5. X 102)(3.3 X 103) Multiply the Coefficients 5 X 3.3 = 16.5 Add the Exponents 102 X 103 = 105 16.5 X 105 BUT 16.5 is not greater than or equal to 1 and less than 10. so we must move the decimal place, 1.65 X 106

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**Practice Page 83 #1,2 Multiplying with Scientific Notation**

(2.2 X 10-2) X (3 X 105) = (-3.2 X 105) X (2.1 X 102) = 6.6x103 -6.72x107

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**Dividing with Scientific Notation**

(3.3 X 104)/ (6.6 X 102) 3.3/ 6.6 = 0.5 Subtract the Exponents 104 / 102 = 102 0.5 X 102 BUT 0.5 is not greater than or equal to 1 and less than 10. 5 X 101 (3.3 X 104)/ (2.3 X 102) 33000 / 230 = Divide the Coefficients 3.3/ 2.3 = Subtract the Exponents 104 / 102 = 102 X 102

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**Dividing with Scientific Notation**

(2.1 X 104) / (8.4 X 103) = (3.1 X 103) / (6.2 X 105) = 2.5 x 100 5 x 10-3

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**Scientific Notation page 84 Addition/Subtraction**

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Homework page 83 # 3-6 page 84 all

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