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Advanced Placement Chemistry Significant Figures Review AP Chemistry 2010 - 2011

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Significant Figures When we use equipment to measure quantities, we are limited in our ability to report an accurate value of the measurement by the precision of the equipment used to measure the quantity. When we report measurements, we want the presented values to have the precision that is possible but not more than is possible or reasonable. Thus, we apply rules for reading equipment and using those measurements in our calculations and reported data (answers).

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Significant Figures For example, look at the burette at right. It is marked in 1 mL increments. Because the burette is marked in 1 mL increments, we can easily read the volume to these markings. Consider that the volume is at the level shown and the burette was initially at the zero mark. What certain volume of solution has been used?

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Although we know for certain that the volume used is 14 mL, we really know that the volume used is between 14 and 15 mL. So, we estimate one additional digit beyond those that are known for certain. Here, we estimate the 0.10 mL value because we know the 1 mL value with certainty. What estimated volume of liquid has been used? Significant Figures

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We report measurements to one additional digit beyond those that are know for certain – these are termed the significant figures of the measurement. We do not report beyond one estimated digit because the estimated digit is just that – estimated; to increase the precision beyond an estimated digit would add no usefulness to the measurement. In fact, it would report false information by implying that we know the value to a greater precision than that which is actually known. For example, we would not report the volume in the previous example to 14.557839200 mL, as this implies much more precision than what is really available to us. Significant Figures

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In essence, we report data to one place beyond the place in which the equipment is marked. So, for a burette marked to the ‘ones’ place, we report to the ‘tenths’ place. For a pipette marked to the ‘tenths’ place, we would estimate the ‘hundredths’ place. Typical laboratory equipment that we use will require estimation to 0.10 or 0.01. Digital equipment is programmed to estimate the last digit – do not try to estimate beyond those that are shown on the display. Significant Figures

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When reading data, how many significant figures are present? All non-zero digits are significant. This measurement has 3 significant figures. Significant Figures

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When reading data, how many significant figures are present? Zeros between non-zero digits are significant. This measurement has 4 significant figures. Significant Figures

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When reading data, how many significant figures are present? Zeros are also significant when a decimal point is present and the zeros are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does it add precision to the measured value?”) This measurement has 3 significant figures. Significant Figures

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When reading data, how many significant figures are present? Zeros are also significant when a decimal point is present and the zeros are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does it add precision to the measured value?”) This measurement has 3 significant figures. Significant Figures

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When reading data, how many significant figures are present? Zeros are also significant when a decimal point is present and the zeros are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does it add precision to the measured value?”) This measurement has 3 significant figures. Significant Figures

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When reading data, how many significant figures are present? Zeros are also significant when a decimal point is present and the zeros are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does it add precision to the measured value?”) This measurement has 4 significant figures. Significant Figures

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When reading data, how many significant figures are present? Zeros are also significant when a decimal point is present and the zeros are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does it add precision to the measured value?”) This measurement has 4 significant figures. Significant Figures

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When reading data, how many significant figures are present? Zeros are also significant when a decimal point is present and the zeros are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does it add precision to the measured value?”) This measurement has 1 significant figure. Significant Figures

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When reading data, how many significant figures are present? Zeros are also significant when a decimal point is present and the zeros are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does it add precision to the measured value?”) This measurement has 1 significant figure. Significant Figures

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When reading data, how many significant figures are present? Zeros are also significant when a decimal point is present and the zeros are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does it add precision to the measured value?”) This measurement has 4 significant figures. Significant Figures

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When reading data, how many significant figures are present? Defined and counted values have an infinite number of significant digits and are not used in determining the overall precision of a reported value. This defined value has INFINITE significant figures. Significant Figures

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When reading data, how many significant figures are present? Defined and counted values have an infinite number of significant digits and are not used in determining the overall precision of a reported value. These counted values have INFINITE significant figures. Significant Figures

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Practice: Indicate the number of significant figures in the following values. 0.056 cm0.111 g3.045 x 10 3 lbs 2 3 4 1.34 meters0.0500 hours4.5 x 10 -4 grams 3 3 2 6.54 g5260 feet in a mile6.022 x 10 23 atoms 3 infinite 4 125.05 grams2.54 cm60 minutes in 1 hour 5 3 infinite 15.9994 grams0. 0540 cm 3 1.0 x 10 2 grams 6 3 2 Significant Figures

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When calculating with data, how do we represent an answer? When adding or subtracting values, we report the answer to contain a number of DECIMAL places equal to the term with the fewest used to obtain the answer. Significant Figures

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When calculating with data, how do we represent an answer? When adding or subtracting values, we report the answer to contain a number of DECIMAL places equal to the term with the fewest used to obtain the answer. Significant Figures

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When calculating with data, how do we represent an answer? When adding or subtracting values, we report the answer to contain a number of DECIMAL places equal to the term with the fewest used to obtain the answer. Significant Figures

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When calculating with data, how do we represent an answer? When adding or subtracting values, we report the answer to contain a number of DECIMAL places equal to the term with the fewest used to obtain the answer. Significant Figures

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When calculating with data, how do we represent an answer? When multiplying or dividing values, we report the answer to contain a number of SIGNIFICANT FIGURES equal to the term with the fewest used to obtain the answer. Significant Figures

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When calculating with data, how do we represent an answer? When multiplying or dividing values, we report the answer to contain a number of SIGNIFICANT FIGURES equal to the term with the fewest used to obtain the answer. Significant Figures

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When calculating with data, how do we represent an answer? When multiplying or dividing values, we report the answer to contain a number of SIGNIFICANT FIGURES equal to the term with the fewest used to obtain the answer. Significant Figures

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When calculating with data, how do we represent an answer? When multiplying or dividing values, we report the answer to contain a number of SIGNIFICANT FIGURES equal to the term with the fewest used to obtain the answer. Significant Figures

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When calculating with data, how do we represent an answer? Rounding: consider only the digit that follows the digit to be retained; round up if it is 5 or greater, round down if it is less than 5. Significant Figures

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When calculating with data, how do we represent an answer? Rounding: consider only the digit that follows the digit to be retained; round up if it is 5 or greater, round down if it is less than 5. Significant Figures

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When calculating with data, how do we represent an answer? Rounding: consider only the digit that follows the digit to be retained; round up if it is 5 or greater, round down if it is less than 5. Significant Figures

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When calculating with data, how do we represent an answer? Sometimes, we can only represent data to the correct number of sig figs if we use scientific notation. Significant Figures

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When calculating with data, how do we represent an answer? Sometimes, we can only represent data to the correct number of sig figs if we include trailing zeros and a decimal point. Significant Figures

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Practice: Perform the following calculations to the correct number of sig figs 0.05 g + 1.04 g0.05 – 1.04 g 1.09 g –0.99 g 0.05 g + 1.0 g0.05 g – 1.0 g 1.1 g –1.0 g 100.0 grams + 10.0 grams0. 05 g + 3.222 g 110.0 g 3.27 g 5.1 kg + 3.672 kg6.0944 g + 32.998 g + 22.989 g 8.8 kg 62.081 g Significant Figures

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Practice: Perform the following calculations to the correct number of sig figs Assume all are measured values unless otherwise indicated 6.345 x 0.0025 3.250 ÷ 200 0.016 0.02 2.50 · 10 2 x 10020 x 20 3 x 10 4 400 20 x 20.20. x 20. 400 4.0 x 10 2 20.0 x 20.020.00 x 20.00 400. 400.0 19.55 days converted to hoursmolar mass of PbCO 3 469.2 hours 267.2 g Significant Figures

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The following items in your textbook will provide additional practice: 1.37 to 1.42 You can also try the Skill Activity on this topic online: AP Chemistry Skill Activities Significant FiguresSignificant Figures

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