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POWERPOINT THE SECOND In which you will learn about: Scientific notation +/-/x/÷ with sig figs Rounding

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To help us with math that is coming up… What is Scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. Scientific notation is a way of expressing really big numbers or really small numbers. For very large and very small numbers, scientific notation is more concise. For very large and very small numbers, scientific notation is more concise.

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Scientific notation consists of two parts: A number between 1 and 10 A number between 1 and 10 A power of 10 A power of 10 N x 10 x

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To change standard form to scientific notation… Place the decimal point so that there is one non-zero digit to the left of the decimal point. Place the decimal point so that there is one non-zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

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Examples Given: 289,800,000 Given: 289,800,000 Use: 2.898 (moved 8 places) Use: 2.898 (moved 8 places) Answer: 2.898 x 10 8 Answer: 2.898 x 10 8 Given: 0.000567 Given: 0.000567 Use: 5.67 (moved 4 places) Use: 5.67 (moved 4 places) Answer: 5.67 x 10 -4 Answer: 5.67 x 10 -4

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To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent 10. Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

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Example Given: 5.093 x 10 6 Given: 5.093 x 10 6 Answer: 5,093,000 (moved 6 places to the right) Answer: 5,093,000 (moved 6 places to the right) Given: 1.976 x 10 -4 Given: 1.976 x 10 -4 Answer: 0.0001976 (moved 4 places to the left) Answer: 0.0001976 (moved 4 places to the left)

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Significant Numbers in Calculations A calculated answer cannot be more precise than the measuring tool. A calculated answer cannot be more precise than the measuring tool. A calculated answer must match the least precise measurement. A calculated answer must match the least precise measurement. Significant figures are needed for final answers from Significant figures are needed for final answers from 1) adding or subtracting 1) adding or subtracting 2) multiplying or dividing

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Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 26.54 answer 26.5 one decimal place

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Multiplying and Dividing Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

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Rounding Rules Always look at the immediate digit to the right of the place you want to round to If the number is <5, round down (keep the digit) If the number is = or >5, round up NO sequential rounding!!!!

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HOMEWORK 1) A. Which answers contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 10 3 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 10 5 1) 535 2) 535,000 3) 5.35 x 10 5

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HW CONT’D 2) State the number of significant figures in each of the following: A. 0.030 m B. 4.050 L C. 0.0008 g D. 3.00 m E. 2,080,000 bees

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HW CONT’D SOME MORE 3) Express these numbers in Scientific Notation: a)405789 b) 0.003872 c) 3000000000 d) 2 e) 0.478260

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Yup, even more HW 4) In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.83) 257 B. 58.925 - 18.2= 1) 40.725 2) 40.733) 40.7

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And some more… 5) A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.32) 11 3) 0.041

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