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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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93,000,000 --- Standard Form 9.3 x 10 7 --- 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. 9.85 x 10 7 6.41 x 10 10 2.79 x 10 8 4.2 x 10 6

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More Practice Problems 1) 734,000,000 = ______ x 10 8 2) 870,000,000,000 = ______x 10 11 3) 90,000,000,000 = _____ x 10 10 On these, decide where the decimal will be moved. 1)7.34 x 10 8 2) 8.7 x 10 11 3) 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 10 4 2) 7.2 x 10 6 3) 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 3.40000 --- move the decimal

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Write in Standard Form 6.27 x 10 6 9.01 x 10 4 6,270,000 90,100

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Positive Exponents 10 1 = 10 10 2 = 10X10= 100 10 3 = 10X10X10 = 1000 10 4 = 10X10X10X10 = 10,000

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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 = 0.0001

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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 10 4 250,000 = 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 0.00006 = 6 X 10 -5 0.00045 = 4.5 X 10 -4 Count places to the right until there is one number to the left of the decimal point 0.003 = ? 0.0000025 = ?

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Multiplying with Scientific Notation Add the Exponents 10 2 X 10 3 = 10 5 100 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 = 10 5 7.59 X 10 5 759,000

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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 = 10 1 10000X 1000 = 10

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Dividing with Scientific Notation (3.3 X 10 4 )/ (2.3 X 10 2 ) 33000 / 230 = 143.4783 Divide the Coefficients 3.3/ 2.3 = 1.434783 Subtract the Exponents 10 4 / 10 2 = 10 2 1.4347823 X 10 2 143.4783

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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 0.2 + 3 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 10 2 + 3.0 x 10 3.2 x 10 3 + 3.0 x 10 3 =.2+3 x 10 3 = 3.2 x 10 3 2.0 x 10 7 - 6.3 x 10 5 2.0 x 10 7 -.063 x 10 7 = 2.0-.063 x 10 7 = 1.937 x 10 7 1. Make exponents of 10 the same 2. Subtract 2.0 -.063 and keep the 10 7 intact

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