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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 Move decimal left Leave only one number in front of decimal

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Step 2 Write number without zeros

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Step 3 Count how many places you moved decimal Make that your power of ten

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

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93,000, Standard Form 9.3 x Scientific Notation

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Practice Problem 1) 98,500,000 = 9.85 x 10 ? 2) 64,100,000,000 = 6.41 x 10 ? 3) 279,000,000 = 2.79 x 10 ? 4) 4,200,000 = 4.2 x 10 ? Write in scientific notation. Decide the power of ten x x x x 10 6

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More Practice Problems 1) 734,000,000 = ______ x ) 870,000,000,000 = ______x ) 90,000,000,000 = _____ x On these, decide where the decimal will be moved. 1)7.34 x ) 8.7 x ) 9 x 10 10

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Complete Practice Problems 1) 50,000 2) 7,200,000 3) 802,000,000,000 Write in scientific notation. 1) 5 x ) 7.2 x ) 8.02 x 10 11

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Scientific Notation to Standard Form Move the decimal to the right 3.4 x 10 5 in scientific notation 340,000 in standard form move the decimal

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Write in Standard Form 6.27 x x ,270,000 90,100

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Positive Exponents 10 1 = = 10X10= = 10X10X10 = = 10X10X10X10 = 10,000

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Negative Exponents = 1/10 = = 1/100 = = 1/1000 = = 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 ,000 = 2.5 X 10 5 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 = 4.5 X Count places to the right until there is one number to the left of the decimal point = ? = ?

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Multiplying with Scientific Notation Add the Exponents 10 2 X 10 3 = X 1000 = 100,000

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Multiplying with Scientific Notation (2.3 X 10 2 )(3.3 X 10 3 ) 230 X 3300 Multiply the Coefficients 2.3 X 3.3 = 7.59 Add the Exponents 10 2 X 10 3 = X ,000

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Multiplying with Scientific Notation (4.6 X 10 4 ) X (5.5 X 10 3 ) = ? (3.1 X 10 3 ) X (4.2 X 10 5 ) = ?

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Dividing with Scientific Notation Subtract the Exponents 10 4 /10 3 = X 1000 = 10

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Dividing with Scientific Notation (3.3 X 10 4 )/ (2.3 X 10 2 ) / 230 = Divide the Coefficients 3.3/ 2.3 = Subtract the Exponents 10 4 / 10 2 = X

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Dividing with Scientific Notation (4.6 X 10 4 ) / (5.5 X 10 3 ) = ? (3.1 X 10 3 ) / (4.2 X 10 5 ) = ?

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Addition and subtraction Scientific Notation 1. Make exponents of 10 the same 2. Add and keep the 10 3 intact The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same. 2.0 x x x x 10 3 =.2+3 x 10 3 = 3.2 x x x x x 10 7 = x 10 7 = x Make exponents of 10 the same 2. Subtract and keep the 10 7 intact

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