Significant Figures

Significant Figures As you know, when you make a measurement, the last digit in a measurement always has some uncertainty. Since all digits in a measurement are certain except for the last one, which digits are important? All of them!

Significant Figures “Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated” (Davis, Frey, Sarquis, and Sarquis 46)

Significant Figures According to this ruler, the measurement is 5.18 cm. Each number in this measurement is significant.

Significant Figure Rules We need to be able to identify the significant figures in a measured value (Davis et al. 46)

Significant Figure Rules All nonzero digits are significant! Examples: 2 cm = 1 significant figure 15 mL = 2 significant figures 418 moles = 3 significant figures 4 207 893 grams = 7 significant figures

Significant Figure Rules Zeros can be tricky though. They can either be significant or insignificant. There are 4 rules.

Significant Figure Rules for Zero (Davis et al. 47) Example Zeros appearing between nonzero digits are significant. 404 mL (3 significant figures) 1.031 km (4 significant figures) Zeros appearing in front of all nonzero digits are not significant. 0.0023 mg (2 significant figures) 0.0000389 m (3 significant figures) Zeros at the end of a number and to the right of a decimal point are significant. 1.20 cm (3 significant figures) 5.4000000 mg (8 significant figures) Zeros at the end of a number but to the left of a decimal point may or may not be significant. Zeros that are placeholders are not significant. A decimal point placed after zeros means the zeros are significant. 300 km (1 or 3 significant figures, depending on which zeros are placeholders) 300. km (3 significant figures – the decimal point makes the zeros significant)

Determine the number of significant figures in each number 1230 km 0.01023 mg 1010 hm 0.00130 mg 100 s 100. s

Rounding with Significant Figures We often have to round calculated values to the appropriate number of significant figures. Example: speed = distance time speed = 10.21 meters 4.04 seconds speed = 2.527 227 723 meters/second The answer contains more digits than allowed by the measurements. We have to round. Answer: 2.53 meters/second (3 significant figures)

Rounding with Significant Figures If the digit to the right of the last significant figure is 5 or greater, round the last significant figure up. If the digit to the right of the last significant figure is 4 or less, keep the last significant figure the same.

Rounding with Significant Figures Example: Round 8.237 kg to three significant figures. 8.237 kg (the underlined “3” is the third significant figure) digit to the right of our last significant figure (7 > 5, therefore, round the “3” to a “4”) 8.237 kg Answer: 8.24 kg

Rounding with Significant Figures Example: Round 1.23 L to 2 significant figures. 1.23 L (the underlined “2” is the second significant figure) digit to the right of our last significant figure (3 < 5, therefore, the “2” remains the same) 1.23 L Answer: 1.2 L

Rounding with Significant Figures Examples: Round 2.18 mL to 2 significant figures. ___________ Round 5.384 4 g/cm3 to 4 significant figures. ____________ Round 3.52 mol to 1 significant figure. ______________ Round 112 km to 2 significant figures. _____________ Round 871 mm to 1 significant figure. ____________

Works Cited Davis, Raymond E., Mickey Sarquis, Regina Frey, and Jerry L. Sarquis. Modern Chemistry: Teacher Edition. Austin: Holt, Rinehart and Winston, 2006. Print.