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S IGNIFICANT F IGURES

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Significant figures Numbers known to have some degree of reliability Critical when reporting scientific data Tell accuracy of measurement For example: Henry is 2 years old. Henry is 23 months old. Henry is 23.25 months old.

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Rules for significant figures 1. All non-zero digits are always significant. (1,2,3,4,5,6,7,8,9) Examples 632 = 3 sig figs 72 = 2 sig figs 2. All zeroes between non-zero numbers are always significant. Examples: 303 = 3 sig figs 70004 = 5 sig figs 60204 = 5 sig figs

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3. All zeroes which are simultaneously to the right of the decimal point AND at the end of the number are always significant. Examples 3.40 = 3 sig figs 7.0 = 2 sig figs 4. Leading zeroes to the left of the first nonzero digit are NOT significant. Examples 0.005 = 1 sig fig 0.012 = 2 sig figs 5. When a number ends in zeroes that are to the left of the decimal, they are not (necessarily) significant. Examples 600 = 1 sig fig 70 = 1 sig fig

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Rules for Addition and Subtraction To determine the number of sig figs in your answer: Count the number of DECIMAL PLACES in the numbers you are adding or subtracting. Your answer cannot contain more decimal places than the smallest number of decimal places in the numbers being added or subtracted. Example 132.45 (2 decimal places) 49.678 (3 decimal places) + 90.3 (1 decimal place) - 8.23 (2 decimal places) 42.15 (calculator answer) 41.448 (calc. answer) = 42.2 (1 decimal place) = 41.45 (2 decimal places)

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Rules for multiplication and division To determine the number of sig figs in your answer Count the number of significant figures in the numbers you are multiplying or dividing. Your answer cannot contain more significant figures than the number being multiplied or divided with the least amount of significant figures. Example 332.46 (5 sig figs) 70.45 (4 sig figs) * 8.29 (3 sig figs) / 8.2 (2. sig figs) 2,756.0934 (calc. answer)8.5914634 (calc. answer) * 2,760* 8.6

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Scientific Notation Used to write really large or really small numbers Instead of writing 4,000,000,000,000, you could write 4.0 x 10 12 Examples: 7,200,000,000 7.2 x 10 9 42,869,238,001,0434.2 x 10 13 0.0000000000088.0 x 10 12 0.0000000456924.5 x 10 8

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How to write in scientific notation Place the decimal point such that there is one non- zero digit to the left of the decimal point (ex. 7.2) Count the number of decimal places the number has moved from the original number. This will be the exponent of 10. 7,200,000 7.2 the decimal moved 6 spaces 7.2 x 10 6 Of the original number was less than zero, the exponent will be negative If the original number was greater than zero, the exponent will be positive

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7.2 x 10 7 = 72,000,000. 7.2 x 10 -7 = 0.00000072

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Rules for adding/subtracting scientific notation: The exponents must have like terms! Add/subtract the coefficients The base and exponent will remain the same 6.2 x 10 7 coefficient base exponent 7.2 x 10 4 + 1.1 x 10 4 = 8.3 x 10 4 9.2 x 10 7 – 3.1 x 10 7 = 6.1 x 10 7

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Rules for multiplying scientific notation Exponents do not have to be the same Multiply the coefficient Add the exponents 3.2 x 10 4 x 2.4 x 10 8 = 7.68 x 10 12 4.5 x 10 4 x 6.4 x 10 7 = 28.8 x 10 11 larger than 10 = 2.88 x 10 12 = 2.9 x 10 12 7.5 x 10 -4 x 1.3 x 10 -6 = 9.75 x 10 -10

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Rules for dividing scientific notation Divide coefficients Subtract exponents 8.2 x 10 7 / 3.4 x 10 5 = 2.4 x 10 2 5.3 x 10 5 / 3.7 x 10 7 = 1.4 x 10 -2 4.2 x 10 -3 / 1.2 x 10 -5 = 3.5 x 10 2

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D IMENSIONAL A NALYSIS A problem solving method used to convert units. Conversion factors Expression for the relationship between units Used to convert units Ex. 1 hour = 60 minutes 1 hour or 60 minutes 60 minutes 1 hour

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If you want to convert a unit, you set up the conversion factors so that the units cancel out 90 minutes = ? Hours 90 minutes x 1 hour 60 minutes 90 minutes x 1 hour = 1.5 hours 60 minutes

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