Significant Figures Definition: The digits in a measurement that have values that are known exactly PLUS one digit that has a value that is estimated.

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Significant Figures -why we use them -rules for sig. figs. -operations with sig. figs.

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Presentation transcript:

Significant Figures Definition: The digits in a measurement that have values that are known exactly PLUS one digit that has a value that is estimated.

Measurements Determine Significance 80 70 60 50 40 30 20 10 Read the temperature on the thermometer. Is it: 75°C? 74°C? 74.2°C? How carefully CAN you read it? The instrument itself determines the significance.

Rules for Determining the number of Significant Figures in a Given Measurement If you are given a measurement (i.e. YOU did not measure it), you follow these rules to calculate the number of sig. figs.: All non-zero digits are sig. figs (ex. 1.2300, 3004) Final zeros to right of decimal are sig. figs (ex. 1.0, 1.2300) Zeros surrounded by significant figures are significant (ex. 1.2300, 102, 3004)

Record Number of Significant Figures in Each Measurement

Rule for Addition and Subtraction with Sig. Figs. Round the sum or difference so that it has the SAME number of DECIMAL PLACES as the measurement having the FEWEST decimal places. ex. 2.7 + 3.52 = 6.22 = correct answer shown in red box; what you get on your calculator shown in italics 6.2 ex. 73 - 2.341 = 70.659 = 71 ex. 1001 - 0.099 = 1000.901 = 1001 ex. 2.94 + 0.06 = 3 = 3.00

Rule for Multiplication & Division with Sig. Figs. Express a product or quotient to the same number of significant figures as the multiplied or divided measurement having the fewer total significant figures. ex. 32.43 • 2.17 = 70.3731= correct answer shown in red box; what you get on your calculator shown in italics 70.4 (3 sig. figs.) ex. 9574  45 = 212.7555556 = 210 (2 sig. figs.)

Round Correctly 1) 4.375 g 14.62 g + 327.9 g 2) 3.0024L - 2.3L = A. 347g B. 346.895g C. 346.9g A. 0.7024 L B. 0.7 L C. 0.70 L

Round Correctly Example 2 Example 1 d = 23 g / 4.44 cm3 = a) 5.18018018 g/cm3 b) 5.18 g/cm3 c) 5.2 g/cm3 d) 5 g/cm3 Example 1 5.22 m x 82.7 m = a) 431.694 m2 b) 432 m2 c) 431.7 m2 d) 430 m2

Infinite Number of Significant Digits Some quantities have an infinite number of significant figures because they are definitions rather than measurements. Example, by definition 1 meter = 100.000 00…..cm

sig·nif·i·cant: Definition: Having or expressing a meaning; meaningful. Why are some “figures” insignificant?