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Significant Figures. A.K.A. “Sig. Figs.”. Significant Figures. 3. 561 m. 2,001 ft. 4. 98.03 mL. 4. 0.005 g. 1. 55.00 cm. 4. 20,000 leagues. 1. All of the digits that are precisely measured Rules: 1. Non-zero digits are significant 2. “Captured” zeros are significant
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Significant Figures A.K.A. “Sig. Figs.”
Significant Figures 3 561 m 2,001 ft 4 98.03 mL 4 0.005 g 1 55.00 cm 4 20,000 leagues 1 • All of the digits that are precisely measured • Rules: 1. Non-zero digits are significant 2. “Captured” zeros are significant 3. “Leading” zeros are NOT significant 4. “Trailing” zeros are • Significant if the number has a decimal point • NOT significant if the number is whole
How many significant figures are in the following measurements? 3 All nonzero 2 Leading zeros = NOT significant 4 Captured zeros = significant 3 Trailing zeros = significant in a decimal 3 Trailing zeros = NOT significant in a whole number 6 5.26 L 0.0031 km 2.051 g 0.0370 ug 5,280 ft 0.00130020 kg
Rules for multiplication and division Example: 26.1 cm x 3.2 cm = 83.52 cm2? Round to 84 cm2 The answer is rounded to the # of sig. figs. Contained in the measurement with the LEAST # of sig. figs.
Rules for addition and subtraction Example: 2.01 cm + 5.1 cm + 3.044 cm 3.044 *The answer may only go out as far as the 10th place 2.01 + 5.1 10.154? 10.2 cm The answer is rounded to the last significant placein the measurement with the least number of significant places
Conversion factors are useful to scientists • Examples: • 4 cups = 1 quart • 1.094 yd = 1 meter • 1 kg = 2.2 lb • Conversion factors have infinite significant figures – they are EXACT and do not impact the # of sig. figs in your answer!
Dimensional Analysis – a way to convert units How many cm are in 3.5 in? 3.5 in • Steps to follow • Rewrite the given quantity • Select the appropriate conversion factor • Multiply the given quantity by the conversion factor *The unit you WANT goes on top *The unit you HAD goes on the bottom • Multiply/divide as necessary, cancel units 1 in = 2.54 cm 3.5 in x = 2.54 cm 8.9 cm 1 in
Dimensional Analysis – a way to convert units How many kg are in 125 lb? 125 lb • Steps to follow • Rewrite the given quantity • Select the appropriate conversion factor • Multiply the given quantity by the conversion factor *The unit you WANT goes on top *The unit you HAD goes on the bottom • Multiply/divide as necessary, cancel units 1 kg = 2.2 lb 1 kg 125 lb x 56.8 kg = 2.2 lb The original measurement Had 3 sig. figs.
Density is a physical property of matter • A physical property of matter • Density = mass volume d = m V • Common units: • g/mL for liquids • g/cm3 for solids
Interesting density facts • Density often changes with temperature • Less dense objects float on denser objects In the popular computer game “Oregon Trail”, an option is to float the wagon across the river.
