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Scientific Notation A short-hand way of writing large and small 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 sure that you write a 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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What about a negative exponent? The sign of the exponent tells which direction to move the decimal. A positive exponent means you move the decimal to the right and a negative exponent means you move the decimal to the left.

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Negative Exponents in Scientific Notation When you have a negative exponent in scientific notation, you will move the decimal point to the LEFT!! 6.345 * 10 ¯ 6 is 0.000006345

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What would the following be in standard form….. 3.45 * 10 ¯ 4 8 * 10 ¯ 8 9.3452 * 10 ¯ 7 7.776 * 10 ¯ 11 2.209 * 10 ¯ 10 0.000345 0.00000008 0.00000093452 0.00000000007776 0.0000000002209

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Turn the following into scientific notation… 0.00002352 0.02147 0.0000085 0.00000000009 0.3 0.98888501 0.00000045

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What is the Exponent? 2.352 * 10 2.147 * 10 8.5 * 10 9 * 10 3 * 10 9.8888501 * 10 4.5 * 10

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