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Add & Subtract with Scientific Notation

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43210 In addition to 3, student will be able to go above and beyond by applying what they know about working with integer exponents. The student will be able to work with integer exponents. - Know and apply the properties of exponents. - Simplify numerical expressions with exponents. - Perform operations with scientific notation. With no help the student has a partial understanding of integer exponents. - Is able to use scientific notation to estimate very large or very small numbers. - Interpret scientific notation generated by technology. With help, the student may have a partial understandin g of how to work with integer exponents. Even with help, the student is unable to work with integer exponents. Focus 11 - Learning Goal: The student will be able to work with integer exponents.

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Scientific Notation Review Scientists very often deal with very small and very large numbers, which can lead to a lot of confusion when counting zeros! Scientific notation is used to represent these values. Convert 1,500,000 to scientific notation: Move the decimal point so that there is only one digit to it’s left, a total of 6 places. 1.5 10 6 Convert 0.000025 to scientific notation. Move the decimal point 5 places to the right. 2.5 10 -5

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Addition and Subtraction with Scientific Notation Before numbers in scientific notation can be added or subtracted, the exponents must be equal. The decimal point is moved in one of the numbers to make the exponents the same. When you move the decimal left, the exponent increases. When you move the decimal right, the exponent decreases.

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Addition and Subtraction with Scientific Notation Let’s change 10 2 to 10 3. Move the decimal on 3.4 to the left. Since the exponent needed to increase by one, the decimal point only needed to move one place to the left. Now that the exponents are the same, add the numbers. (0.34 + 4.57) 10 3 = 4.91 10 3

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Addition and Subtraction with Scientific Notation Practice 1.(1.2 10 5 ) + ( 5.35 10 6 ) 1.Change 10 5 to 10 6 2.Move the decimal on 1.2 one place left. 3. (0.12 10 6 ) + ( 5.35 10 6 ) 4.(0.12 + 5.35) 10 6 = 5. 5.47 10 6 2. (6.91 10 -2 ) + ( 2.4 10 -3 ) 1.Change 10 -3 to 10 -2 2.Move the decimal on 2.4 one place left. 3. (6.91 10 -2 ) + ( 0.24 10 -2 ) 4.(6.91 + 0.24) 10 -2 = 5. 7.15 10 -2

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Addition and Subtraction with Scientific Notation Practice 3.(3.67 10 2 ) – (1.6 10 1 ) 1.Change 10 1 to 10 2 2.Move the decimal on 1.6 one place left. 3. (3.67 10 2 ) - (0.16 10 2 ) 4.(3.67 – 0.16) 10 2 = 5. 3.51 10 2 4. (8.41 10 -5 ) - (7.9 10 -7 ) 1.Change 10 -7 to 10 -5 2.Move the decimal on 7.9 two places left. 3. (8.41 10 -5 ) - ( 0.079 10 -5 ) 4.(8.41 - 0.079) 10 -5 = 5. 8.331 10 -5

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