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10795-97155Mind Blowing Significant Figures00Mind Blowing Significant Figures4-page entry…Seed Questions: What is the area of a 3 cm by 4 cm rectangle?Exploration: Write kind of small. The knee jerk mathematical answer to the SQ is __________.But is this the best answer?How well do we know this answer?Suppose that the sides of this rectangle were only measured to the nearest centimeter. What is the smallest this area could actually be, if you rounded the side measurements to 3 cm by 4 cm starting with 2 sig figs? Hint: one side could be 2.5 cm. Show calc.What is the largest this area could actually be? Show calc.The range of possible areas is:What is the single, most honest numerical value for the area?But isn’t 12 cm2 more accurate?Second page…Let’s make this a matter of life and death. You are trapped in a submarine resting on the bottom of a freshwater bay. The density of water around your sub is 0.998 g/cm3. You want to release something with the sub’s name on it that will float, to aid in your rescue. You happen to have a hollow metal block that has a mass of 39.85 g. You use a centimeter stick as shown to get the dimensions. Record the dimensions to 1 sig fig. Paste these photos into your PJ.159607310636300-24701510604500334264011620500 2540216535L =W =H =(1 sig fig)00L =W =H =(1 sig fig)Do you expect your block will sink or float? Begin with all the numbers your calculator gives you, then round appropriately.Sounds like you need more precise measurements. Here they are. Record the dimensions to 2 sig figs. Again, paste photos into your PJ.198384715970300424095514816700-33782014859000273685155998L =W =H =(2 sig figs)00L =W =H =(2 sig figs)Calculate the volume and the density.Now do you expect your block will sink or float? Again, begin with all the numbers your calculator gives you, then round appropriately.Third page…What? You want more precision? OK. Here it is. Record the caliper dimensions to 3 sig figs. Paste these images too.-3632201911350019907255291004336732434100273685134620L =W =H =(3 sig figs)00L =W =H =(3 sig figs)Calculate the volume and the density again.What do you conclude about whether your block will sink or float? Again, begin with all the numbers your calculator gives you, then round appropriately.Fourth page…Time to test your conclusion above. Did your block sink or float?Big Idea: Sig figs can save you time, money, and maybe your life.There are 3 types of numerical values:TypeHow well do you know it?# of Sig FigsMeasured Quantities:ApproximatelyNumber variesDefined Quantities:ExactlyInfiniteInteger Counting:ExactlyInfinite sProduct/Quotient Rule: Go with the least number of sig figs in a product or quotient.Example: 2.0 ÷ 3 = 0.7 (1 sig fig in answer)Addition/Subtraction Rule: Line up the decimal places.Example: 25 – 0.3 = 25.? - 0.3 25.? → = 25It is best to avoid interim rounding: round to the appropriate sig figs at the end:(25 – 1.6) 2.455 = (23.4) (2.455) = (57.447) → = 57Discussion: ................
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