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Significant Figures & Measurement

Significant Figures & Measurement. How do you know where to round?. In math, teachers tell you In science, we use significant figure rules. Figuring Out the Rules. “47.6 cm” has 3 sigfigs “3.981 cm” has 4 sigfigs “25 cm” has 2 sigfigs So… what can we say about that?. Rule #1.

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Significant Figures & Measurement

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  1. Significant Figures & Measurement

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

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

  4. Rule#1 All non zero digits are significant.

  5. Practice • “163.4 cm” has ____ sigfigs. • “28” has ____ sigfigs.

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

  7. Rule#2 Sandwich zeros are always significant.

  8. Practice • “20.05 cm” has ____ sigfigs. • “201” has ____ sigfigs.

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

  10. Rule#3 Leading zeros are never significant.

  11. Practice • “0.0065 cm” has ____ sigfigs. • “0.02003” has ____ sigfigs.

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

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

  14. Practice • “25,000 cm” has ____ sigfigs. • “320.00 cm” has ____ sigfigs.

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

  16. Rounding to a # of Sig Figs • 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

  17. So, what about rounding? • When doing calculations, the final answer must contain the least number of sigfigs. • Example: (2.07 cm)(0.045 cm) = ? • Calculator says: 0.09315 cm2 • 2.07 has 3 sigfigs, 0.045 has 2 sigfigs • We use 2 sigfigs in our answer (least!) • So, 0.093 cm2 is correct!

  18. More Practice • (0.20 cm)(5.66 cm) = ? • (35.01 cm)(0.2 cm) = ? • (0.0071 cm)(95,000 cm) = ? 1.1 cm2 7 cm2 670 cm2

  19. So, what about rounding? • When doing addition and subtraction, the final answer must contain the least number of sigfigs – to the position of the decimal place. • Example: 3.1417cm + 12.7cm = ? • Calculator says: 15.8417 cm • 3.1417 has 5 sigfigs, 12.7 has 3 sigfigs • We cannot be more precise than the tenths place(least!) • So, 15.8 cm is correct!

  20. More Practice • 1.12cm + 2.5cm= ? • 14.135 + 12.7cm = ? • 98.2564cm + 128.34cm = ? 3.6 cm 26.8 cm 226.60 cm

  21. Any questions?

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