Significant Figures

Significant figures All digits in a measurement that are known for certain, plus the first estimated (uncertain) digit Sig figs give an indication of the degree of precision for a measurement and/or calculation

Sig Fig rules – KNOW AND USE THEM Rules for determining how many sig figs are in a measurement: All non-zero values ARE significant i.e. 54 mm has 2 sig figs 5400 m has 2 sig figs All zeros between non-zero digits ARE significant i.e. 504 N has 3 sig figs For numbers less than 1 Zeros directly after the decimal point are not significant i.e. 0.00565 J has 3 sig figs

Sig Fig rules – KNOW AND USE THEM Rules for determining how many sig figs are in a measurement: ctd A zero to the right of a decimal AND following a non-zero digit IS significant 0.150 m has 3 s.f. 15.0 kg has 3 s.f. All other zeros are NOT significant

Scientific Notation & Sig Figs Use scientific notation when you need to specify how many zeros are significant: i.e. write 1500 N with 3 s.f. The best way to do this is with scientific notation: 1.50 x 103 N Write 10600 kg with 4 s.f.

Sig figs in problems Many problems will have values that look like they only have 1 s.f. Assume that all digits in the problems are significant i.e. if a problem says that and object has a mass of 100 kg, please treat that as 3 s.f.

Sig. Figs in calculations When adding/subtracting: Your answer must have the same degree of precision as the least precise measurement (choose the smallest number of decimal places) i.e.: 24.2 g + 0.51g + 7.134g = 31.844 g →31.8 g When multiplying/dividing: The number of sig figs in the answer is equal to the least number of sig figs in any of the measurements used in the calculation i.e.: 3.22 cm x 12.34 cm x 1.8 cm = 71.52264 cm3 → 72 cm3

How many sig figs in each of the following? Examples/ Homework How many sig figs in each of the following? 415.2 cm 0.00065 s 1500 g 0.007250 W 105.00 cm 15.035 cm 0.0560 s 35000 kg 1.25 cm + 6.5 cm + 11.75 cm + 0.055 cm 2.32 mL + 2.2 mL + 0.003 mL + 72.55 mL 36.5 g + 65.22 g + 9.870 g 5.85 kg x 4.257 kg x 7.3 kg 25.50 m x 12.057 m x 0.095m 25.32 mL x 6.87 mL x 35.7 mL

Metric Conversions

Converting in the Metric System Larger prefix – decimal moves left Smaller Prefix – decimal moves right 1 mi = .62 km 1 kg = 2.2 lbs 1 mL = 1 cm3 See handout – Copy into notebook/notes

Practice Convert 75 mL to cm3 Convert 350 mL to L Convert 500 m to Km Convert 0.050 Kg to g Convert 5.0 x 103 mL to L Convert 100 mL to L Convert 600 Kg to g Which two of these are equivalent lengths? 60 mm 0.600 m 6000 cm 0.060 Km In metric, the base unit for length is the ______. In the metric system, the base unit for mass is the ______. The measure of the amount of 3-D space that an object occupies is known as ________. Which of the following are equivalent lengths? 450 cm 45,000 mm 45 m 45,000 Km Which of these is the shortest length? 60 mm 0.060 Km 0.600 m 6000 cm Which of the following is the largest mass? 1000 mg 5 Kg 800 cg 100 g Which metric distance is equal to 0.62 miles? 1 mm 1 cm 1 Km 1 m Which of the following conversions is/are incorrect? 1 Km = 1000 m 1 m = 1000 mm 500 cm = 0.5 m 100 mm = 1 cm Which of the following metric masses is approximately equal to 2.2 pounds? 1 mg 1 Kg 1 µg 1 g  How many millimeters are in one kilometer? How many milliliters are in one deciliter?