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**Scientific Notation 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**

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 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, Standard Form 9.3 x Scientific Notation

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**Practice Problem -----> -----> -----> ----->**

Write in scientific notation. Decide the power of ten. 98,500,000 = 9.85 x 10? 64,100,000,000 = 6.41 x 10? 279,000,000 = 2.79 x 10? 4,200,000 = 4.2 x 10? 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> -----> 4.2 x 106

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**More Practice Problems**

On these, decide where the decimal will be moved. 734,000,000 = ______ x 108 870,000,000,000 = ______x 1011 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 7.34 x 108 2) 8.7 x 1011

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**Complete Practice Problems**

Write in scientific notation. 50,000 7,200,000 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

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**Scientific Notation to Standard Form**

Move the decimal to the right 3.4 x 105 in scientific notation move the decimal ---> 340,000 in standard form

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**Move the decimal to the right.**

Write in Standard Form Move the decimal to the right. 6.27 x 106 9.01 x 104 6,270,000 90,100

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**Positive Exponents 101 = 10 102 = 10X10= 100 103 = 10X10X10 = 1000**

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**Negative Exponents 10-1 = 1/10 = 0.1 10-2 = 1/100 = 0.01**

10-3 = 1/1000 = 0.001 10-4 = 1/10000 =

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Scientific Notation We use the idea of exponents to make it easier to work with large and small numbers. 10,000 = 1 X 104 250,000 = 2.5 X 105 Count places to the left until there is one number to the left of the decimal point. 230,000 = ? 35,000 = ?

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**Scientific Notation Continued**

= 6 X 10-5 = 4.5 X 10-4 Count places to the right until there is one number to the left of the decimal point 0.003 = ? = ?

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**Multiplying with Scientific Notation**

Add the Exponents 102 X 103 = 105 100 X 1000 = 100,000

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**Multiplying with Scientific Notation**

(2.3 X 102)(3.3 X 103) 230 X 3300 Multiply the Coefficients 2.3 X 3.3 = 7.59 Add the Exponents 102 X 103 = 105 7.59 X 105 759,000

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**Multiplying with Scientific Notation**

(4.6 X 104) X (5.5 X 103) = ? (3.1 X 103) X (4.2 X 105) = ?

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**Dividing with Scientific Notation**

Subtract the Exponents 104/103 = 101 10000X 1000 = 10

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**Dividing with Scientific Notation**

(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**

(4.6 X 104) / (5.5 X 103) = ? (3.1 X 103) / (4.2 X 105) = ?

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**Addition and subtraction Scientific Notation**

2.0 x x 103 .2 x x 103 = .2+3 x 103 = 3.2 x 103 1. Make exponents of 10 the same 2. Add and keep the 103 intact The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same. 2.0 x x 105 2.0 x x 107 = x 107 = x 107 1. Make exponents of 10 the same 2. Subtract and keep the 107 intact

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1. Scientific Notation Every positive number X can be written as:

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