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Scientific Notation

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Consists of two parts 1. mantissa The full size number that comes before x 10 2. characteristic The exponent that comes after x 10 and is superscript

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Scientific Notation Example: 3.00 x 10 15 Mantissa Characteristic

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Scientific Notation To convert a normal number to scientific notation, move the decimal either to the left or right until you have a mantissa which is greater than -10 or less than +10

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Scientific Notation If the absolute value of the number is smaller than 1, the characteristic will be negative If the absolute value of the number is larger than 1, the characteristic will be positive

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Scientific Notation Example: 542 The absolute value of the number is greater than one so the characteristic is positive 542 Moved to the left two spaces 5.42 x 10 2

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Scientific Notation Example: -45000000 The absolute value of the number is greater than one so the characteristic is positive -45000000 Moved to the left seven spaces -4.5 x 10 7

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Example: 0.0040 The absolute value of the number is less than one so the characteristic is negative 0.0040 Moved to the right three spaces 4.0 x 10 -3

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Example: -0.209 The absolute value of the number is less than one so the characteristic is negative -0.209 Moved to the right one space -2.09 x 10 -1

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Example : 9.245 The absolute value of the number is between -10 and +10. 9.245 The decimal is not moved. In this case, the characteristic is zero. 9.245 x10 0

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Let’s Practice Change 47600000 into scientific notation. = 4.76 x 10 7

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Let’s Practice Change 0.0890 into scientific notation. = 8.90 x 10 -2

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Let’s Practice Change 50000 into scientific notation. = 5 x 10 4

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Let’s Practice Change 50000. into scientific notation. = 5.0000 x 10 4

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Let’s Practice Change 0.000005454 into scientific notation. = 5.454 x 10 -6

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Expanding Scientific Notation to Regular notation If the characteristic is positive, move the decimal to the right. If the characteristic is negative, move the decimal to the left.

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Expanding Scientific Notation to Regular notation Example 6.50 x 10 2 The characteristic tells us to move two places to the right. 650.

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Expanding Scientific Notation to Regular notation Example 6.50 x 10 -2 The characteristic tells us to move two places to the left. 0.0650

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Let’s Practice Convert 9.7 x 10 -2 into regular notation. 0.097

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Let’s Practice Convert 9.7 x 10 2 into regular notation. 970

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Let’s Practice Convert 5.60 x 10 2 into regular notation. 560.

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Let’s Practice Convert 6.02 x 10 23 into regular notation. 602,000,000,000,000,000,000,000 Isn’t scientific notation great?

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Fixing Incorrect Scientific Notation Fix the mantissa by moving the decimal Add the “fixed” characteristic to the original characteristic

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Example 20.4 x 10 6 (incorrect) Moved over one space to the left (+) to correct the mantissa 2.04 x 10 (6+1) 2.04 x 10 7 (correct)

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Example 200.4 x 10 -6 (incorrect) Moved over two spaces to the left (+) to correct the mantissa 2.004 x 10 (-6+2) 2.004 x 10 -4 (correct)

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Example 0.00340 x 10 8 (incorrect) Moved over three spaces to the right (-) to correct the mantissa 3.40 x 10 (8 + -3) 3.40 x 10 5 (correct)

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Example 0.00340 x 10 -8 (incorrect) Moved over three spaces to the right (-) to correct the mantissa 3.40 x 10 (-8 + -3) 3.40 x 10 -11 (correct)

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Practice Fix the following incorrect number. 0.000579 x 10 11 5.79 x 10 (-4 + 11) 5.79 x 10 7 (correct)

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Practice Fix the following incorrect number. 0.040 x 10 -4 4.0 x 10 (-2 + -4) 4.0 x 10 -6 (correct)

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Practice Fix the following incorrect number. 770.040 x 10 -9 7.70040 x 10 (2 + -9) 7.70040 x 10 -7 (correct)

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Practice Fix the following incorrect number. 65070.0 x 10 3 6.50700 x 10 (4 + 3) 6.50700 x 10 7 (correct)

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