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Significant Figures & Measurement

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How do you know where to round? In math, teachers tell you In math, teachers tell you In science, we use significant figure rules In science, we use significant figure rules

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Figuring Out the Rules “47.6 cm” has 3 sigfigs “47.6 cm” has 3 sigfigs “3.981 cm” has 4 sigfigs “3.981 cm” has 4 sigfigs “25 cm” has 2 sigfigs “25 cm” has 2 sigfigs So… what can we say about that? So… what can we say about that?

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Rule #1 All non zero digits are significant.

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Practice “163.4 cm” has ____ sigfigs. “163.4 cm” has ____ sigfigs. “28” has ____ sigfigs. “28” has ____ sigfigs. 893.27 has ____sigfigs. 893.27 has ____sigfigs. 4 2 5

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Figuring Out the Rules “203 cm” has 3 sigfigs “203 cm” has 3 sigfigs “6.004 cm” has 4 sigfigs “6.004 cm” has 4 sigfigs “50.093 cm” has 5 sigfigs “50.093 cm” has 5 sigfigs So… what can we say about that? So… what can we say about that?

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Rule #2 Sandwiched zeros are always significant.

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Practice “20.05 cm” has ____ sigfigs. “20.05 cm” has ____ sigfigs. “201” has ____ sigfigs. “201” has ____ sigfigs. “803.27” has ____sigfigs. “803.27” has ____sigfigs. 4 3 5

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Figuring Out the Rules “0.004 cm” has 1 sigfig “0.004 cm” has 1 sigfig “0.0203 cm” has 3 sigfigs “0.0203 cm” has 3 sigfigs “0.16 cm” has 2 sigfigs “0.16 cm” has 2 sigfigs So… what can we say about that? So… what can we say about that?

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Rule #3 Leading zeros are never significant.

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Practice “0.0065 cm” has ____ sigfigs. “0.0065 cm” has ____ sigfigs. “0.02003” has ____ sigfigs. “0.02003” has ____ sigfigs. “0.837” has ____sigfigs. “0.837” has ____sigfigs. 2 4 3

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Figuring Out the Rules “20 cm” has 1 sigfig “20 cm” has 1 sigfig “20. cm” has 2 sigfigs “20. cm” has 2 sigfigs “340 cm” has 2 sigfigs “340 cm” has 2 sigfigs “340.0 cm” has 4 sigfigs “340.0 cm” has 4 sigfigs So… what can we say about that? So… what can we say about that?

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Rule #4 Zeros at the end (trailing zeros) are only significant when there is a decimal point somewhere in the number.

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Practice “25,000 cm” has ____ sigfigs. “25,000 cm” has ____ sigfigs. “320.00 cm” has ____ sigfigs. “320.00 cm” has ____ sigfigs. “430. cm” has ____ sigfigs. “430. cm” has ____ sigfigs. 2 5 3

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Significant Figure Rules 1. All nonzero digits are significant. 2. Sandwich zeros are always significant. 3. Leading zeros are never significant. 4. Trailing zeros are only significant when there is a decimal point somewhere in the number.

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Rounding to a # of Sig Figs At the end of your calculation, the calculator says “6848.5973” At the end of your calculation, the calculator says “6848.5973” –To 1 sig fig: –To 2 sig figs: –To 3 sig figs: –To 4 sig figs: –To 5 sig figs: 7000 6800 6850 6849 6848.6

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So, what about rounding? When doing calculations, the final answer must contain the least number of sigfigs. When doing calculations, the final answer must contain the least number of sigfigs. Example: (2.07 cm)(0.045 cm) = ? Example: (2.07 cm)(0.045 cm) = ? Calculator says: 0.09315 cm 2 Calculator says: 0.09315 cm 2 2.07 has 3 sigfigs, 0.045 has 2 sigfigs 2.07 has 3 sigfigs, 0.045 has 2 sigfigs We use 2 sigfigs in our answer (least!) We use 2 sigfigs in our answer (least!) So, 0.093 cm 2 is correct! So, 0.093 cm 2 is correct!

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More Practice 1. (0.20 cm)(5.66 cm) = ? 2. (35.01 cm)(0.2 cm) = ? 3. (0.0071 cm)(95,000 cm) = ? 1.1 cm 2 7 cm 2 670 cm 2

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More on rounding Round 150.093 to two significant figures Round 150.093 to two significant figures Start from left, count two figures Start from left, count two figures Look to the right of the second, Look to the right of the second, Is it 5 or more, round up Is it 5 or more, round up Make sure you leave zeros to place the decimal! (don’t truncate) Make sure you leave zeros to place the decimal! (don’t truncate) 15 does NOT = 150.093, it’s not even close…150.093=150! 15 does NOT = 150.093, it’s not even close…150.093=150!

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Any questions?

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I got one: What about adding/subracting? Joke, get it?

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Figuring Out the Rules 47.6 cm 13.348 cm 47.6 cm 13.348 cm +3.981 cm-11.3 cm +3.981 cm-11.3 cm =51.6 cm = 2.0 cm =51.6 cm = 2.0 cm So… what can we say about that? So… what can we say about that?

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Adding & subtracting Use the least amount of decimal places. Don’t round until you are done calculating!

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Practice 12.345+13.65 12.345+13.65 =26.00 =26.00 2.3 - 1.21 2.3 - 1.21 Calculator says 1.0900.. Calculator says 1.0900.. =1.1 =1.1

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Point to ponder 2.5 x 10 9 +2.300 x 10 3 2.5 x 10 9 +2.300 x 10 3 =2.5 x 10 9 =2.5 x 10 9 Another Another 3.0 x 10 8 – 23,0000 3.0 x 10 8 – 23,0000 = 3.0 x 10 8 = 3.0 x 10 8

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It’s what significant means. 2.5 x 10 9 is way bigger than 2.345 x 10 3 2.345 x 10 3 is insignificant compared to 2.5 x 10 9, it is smaller than the uncertainty in 2.5 x 10 9 2,500,000,000 (uncertainty is +/-50,000,000!) +2,345 2,500,002,345 2.5 x 10 9

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Last one 1.50 x 10 6 +2.345 x 10 5 1.50 x 10 6 +2.345 x 10 5 1.50 x 10 6 1.50 x 10 6 +0.2345 x 10 6 +0.2345 x 10 6 =1.73 x 10 6 =1.73 x 10 6 Make the exponents the same, youll need to move the decimal!

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What’s the rule Line up the decimals Line up the decimals In scientific, that means make them both have the same exponent (the bigger one) In scientific, that means make them both have the same exponent (the bigger one) Done Done

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