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Measurements: Every measurement has UNITS. Every measurement has UNCERTAINTY.

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**Accuracy and Precision in Measurements**

Accuracy: how close a measurement is to the accepted value. Precision: how close a series of measurements are to one another or how far out a measurement is taken. A measurement can have high precision, but not be as accurate as a less precise one.

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**Precision can also mean**

The number of decimal places assigned to the measured number (The more decimal places, the more precise the measurement) Ex. 2.1 cm 2.10 cm 2.100 cm

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**the digit farthest to the right is considered to be estimated.**

Significant Figures are used to indicate the precision of a measured number or to express the precision of a calculation with measured numbers. In any measurement the digit farthest to the right is considered to be estimated. 1 2 2.0 1.3

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**Sig. Fig. Rules (with measurements):**

1. All non-zero digits are significant. 3 sig figs sig figs sig figs 2. Zeros at the beginning of a measurement are not significant. sig fig sig figs sig figs

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**3. Zeros in between two significant figures are significant**

sig figs sig figs 4. Final zeros after a decimal point are significant sig figs sig figs sig figs sig figs sig figs sig figs Counted numbers and definitions (2.54 cm = 1 inch) are considered to be exact and have no effect on the number of sig. figs. reported in calculations with measurements.

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**significant to the 0.1 place**

Calculations with sig. Figs. Addition and subtraction: Look at decimal places! Answer should have the same amount of decimal places as the measurement with the least amount cm cm cm cm = cm significant to the 0.1 place

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**Measurement Calculations with scientific notation.**

Addition/subtraction: must be placed into the same notation. (2.3 x 103) + (3.2 x 104) = 0.23 x 104 x 104 3.43 x 104 = 3.4 x 104

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**Calculations with Sig. figs.**

Multiplication and division (measurements): Count sig figs!! Answer should have the same amount of sig figs as the measurement with the least amount. 2.734 cm x 5.2 cm x cm = cm3 4 s.f. 2 s.f. 5 s.f. written as 120 cm3 2 s.f.’s

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**1. The term that is related to the reproducibility (repeatability) of a measurement is**

a. accuracy. b. precision. c. qualitative. d. quantitative. e. property. Let’s take a “Quiz” b. precision. 2. The number of significant figures in the mass measured as g is a. 1. b. 2. c. 3. d. 4. e. 5. e. 5.

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**3. The number of significant figures in 6.0700 x 10-4… is**

d. 6. e. 7. c. 5. 4. How many significant figures are there in the value ? a. 7 b. 6 c. 5 d. 4 e. 3 d. 4

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**Percent Error your value accepted value**

Indicates accuracy of a measurement your value accepted value

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**Percent Error % error = 2.9 %**

A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 %

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