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Measurement Class 3

Measurement Class 3. OB: defining and understanding significant figures in measuring and in math equations. Handout: The Significance of Significant Figures.

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Measurement Class 3

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  1. Measurement Class 3 OB: defining and understanding significant figures in measuring and in math equations. Handout: The Significance of Significant Figures.

  2. Significant figures are the numbers in our math that are important enough to count. They have real, or significant, value to the measurement. We will measure so many things in chemistry, and we’ll use so many formulas, we need to learn how to deal with the numbers. The rules to significant figures is how we’ll do so. Officially, significant figures is defined this way: In a measurement, all numbers you know, plus one estimated number, are significant.

  3. You want to be sure that your measurements are as correct as possible. You never want to round away how exact you can be. You also are not permitted to be magically more exact than your tool will let you. For instance, 6 grams is not really the same as 6.0 grams, or 6.00 grams, or 6.000 grams. The are all measured to different levels of exactness.

  4. If we are going to measure the temperature in this room right now, with our centigrade thermometer, let’s look at the tool now. What temperature is it? This tool indicates temperature in degrees centigrade. Whole degrees.

  5. With tools that we read with our eyes, like a thermometer, or a ruler, we measure to the closest measure, then estimate out ONE more place. Our eyes can estimate one place, but not two or three more decimal points. You can’t be “more accurate” than your tool let’s you. You should never give up how exact you can be, (don’t just say it’s 20 degrees centigrade, estimate to the tenth of a degree.

  6. Let’s look over these rules on the back of this handout and see if we can’t figure out what this is all about. For any measures: 1. Any digit 1-9 is going to be significant (it’s important and we need to keep track of how many SF we have). How many significant figures in these temperatures? Which is most/least exact? 23°C 23.1°C 23.39°C

  7. For any measures: 1. Any digit 1-9 is going to be significant (it’s important and we need to keep track of how many SF we have). How many significant figures in these temperatures? Which is most/least exact? 23°C 23.1°C 23.39°C 2 SF 3 SF 4 SF Least exact Most exact

  8. 2. If there is a ZERO digit between significant figures, that is significant too. (it’s not just a placeholder) How many SF are in these measures? 101 grams 4509 joules 20,445,567 kilocalories 110 grams 4590 joules 21,445, 567 kilocalories 20,456,056 seconds

  9. 2. If there is a ZERO digit between significant figures, that is significant too. (it’s not just a placeholder) How many SF are in these measures? 101 grams 4509 joules 20,445,567 kilocalories 110 grams 4590 joules 21,445, 567 kilocalories 20,456,056 seconds 3 SF 4 SF 8 SF 3 SF 2 SF 8 SF 8 SF

  10. 3. Zeros before SF are not significant (they are placeholders) How many SF in these measures? 0.0054 kilograms 0.000000000000001 kilo-pascals 0.565 grams

  11. 3. Zeros before SF are not significant (they are placeholders) How many SF in these measures? 0.0054 kilograms (2SF) 0.000000000000001 kilo-pascals(1 SF) 0.565 grams (3SF)

  12. 4. Zeros with a decimal point or without a decimal point (the dot counts!) 150 grams has a zero at the end, and this means we are SURE of 1 one hundred, and 5 tens of grams, but not too sure of the rest. This means it has 2 SF If the measure is 150. grams, that’s different. We are now sure of all three digits. 3 SF

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  14. What about these measures, how many sig figs? 250 tons 340. grams 55,678,900 seconds 1,000,000. inches

  15. What about these measures? • 250 tons 2 SF • 340. grams 3 SF • 55,678,900 seconds 6 SF • 1,000,000. inches 7 SF

  16. 5. Zeros at the end of a decimal number are significant, these ARE NOT PLACEHOLDERS, but indicate you measured to that decimal place and found it to contain NO digits. 1.50 grams 2.0 seconds 98,754, 123.00 grams 0.0040 days

  17. 5. Zeros at the end of a decimal number are significant, these ARE NOT PLACEHOLDERS, but indicate you measured to that decimal place and found it to contain NO digits. 1.50 grams 2.0 seconds 98,754, 123.00 grams 0.0040 days • 2 SF 3 SF • 2 SF • 10 SF

  18. Unlimited Significant Figures This unusual situation will occur when ever we use EQUALITIES, especially when converting from one unit to another. For example, if we were to ask how many SF are in this: 1 pound = 454 grams If you measure 1 pound, it has 1 SF, if you measure 454 grams, that’s 3 SF. Because they are equal to each other, they have unlimited SF…

  19. That’s because 1 pound = 454 grams Means 1.0 pounds = 454.0 grams Or 1.00000… pounds = 454.000000… grams(to the nth degree) That last zero on the end would be significant, and all the zeros in between would be too, so equalities never “limit” SF.

  20. Also, some measures just don’t come in decimal measures, so we “understand” them to have unlimited SF as well. Such as there are four legs on a dog. If it’s a real dog, then it has to have 4 legs, which could also be understood to be 4.000… legs. What else could it be??? Nothing! A piano has 88 keys*** this one is trickier!

  21. In a math equations, the answers must not gain or lose SF. You can’t get MORE EXACT because you multiply or divide, nor should you round away how well you have measured. If you measure your room to be 7.7 meters X 5.4 meters, you need a rug of 41.58 m2 Not really. If you only measure to 2 SF because that’s the limit of your tool, your answer can only have 2 SF. Round the 41.58 m2 to 42 m2 to be correct.

  22. Last rule… When using scientific notation, only the front part (the coefficient) has SF. 6.02 x 1023 atoms has only 3 SF (the 6.02 )

  23. Practice (talk together) How many SF in these measures? 123 m _____ 40.506 cm _____ 0.345 g _____ 30.0 seconds _____ 22 Liters _____ 22.4 liters _____ 0.07080 kg ______ 9.7 x 107 years ______ 9.70 x 107 years _____

  24. Practice (talk together) How many SF in these measures? 123 m 3 SF 40.506 cm 5 SF 0.345 g 3 SF 30.0 seconds 3 SF 22 Liters 2 SF 22.4 liters 3 SF 0.07080 kg 4 SF 9.7 x 107 years 2 SF 9.70 x 107 years 3 SF

  25. Density is the relationship between mass and volume of a substance. (how much stuff divided by how much space it takes). The formula is d=m/v If your unknown metal has mass of 11.46 grams and volume of 1.15 cm3, what is the density? 11.46 g1.15 cm3 D = = 9.9652173 g/cm3 ??? Round to only 3 SF!!! 9.97 g/cm3

  26. Density is the relationship between mass and volume of a substance. (how much stuff divided by how much space it takes). The formula is d=m/v If your unknown metal has mass of 35.46 grams and volume of 7.75 cm3, what is the density?

  27. If your unknown metal has mass of 35.46 grams and volume of 7.75 cm3, what is the density? 35.46 g7.75 cm3 D = = 4.57548387 g/cm3 ??? Round to only 3 SF!!! 4.58 g/cm3

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