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Significant Digits and Measurement Techniques

marius avatar
marius
29 diapositives · 456 Views · Dec 20, 2012

Significant digits and measurement accuracy in scientific calculations, including rules for identifying significant zeros and applying them correctly in multiplication, division, addition, and subtraction.

#significant digits #measurements #estimation #mathematical operations #digital devices #scaled devices #accuracy #rounding
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Significant Digits and Measurement Techniques
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  1. Chapter 2 Significant Digits

  2. Taking Measurements • All measurements involve one estimation. • If the measuring device is digital it will take the estimation for you.

  3. Electronic Measuring Devices • Digital readout measuring diameter of 1.0420 inches. • The last zero is the estimated digit.

  4. Taking Measurements • All measurements involve one estimation. • If the measuring device is scaled you must take the estimation yourself.

  5. Scaled Measuring Devices

  6. Scaled Measuring Devices • Bottom ruler gives a measurement of 8.? cm.

  7. Scaled Measuring Devices • Measure the length of the metal using the top ruler.

  8. How to read a meniscus.

  9. Read the Volume in mL

  10. Significant Digits

  11. Rules for Significant Digits • All non-zero digits are significant. • “Trailing”zeros after the decimal point ARE significant. • Zeros between significant digits are significant. • All other zeros are NOT significant unless indicated to be so by having a bar placed over them.

  12. How to Determine Significant Digits • Underline the leftmost nonzero digit. • Use the rules for significant digits to determine the rightmost significant digit. • Every digit in between the leftmost and rightmost significant digits are significant as well.

  13. Counting or Exact Numbers

  14. 70.12 L 0.000800 mg 82.003 µm 27.0 km 50 people 1.002 cm 200 kg -270.8 ºC 1000 mL 42,729.00 cm 225 beans 99.294 dm 0.06900 m 3,200,000 µL Determine the Significant Digits(Examples in Notebook)

  15. 70.12 L 4 0.000800 mg 3 82.003 µm 5 27.0 km 3 50 people infinite 1.002 cm 4 200 kg 2 -270.8 ºC 4 1000 mL 1 42,729.00 cm 7 225 beans infinite 99.294 dm 5 0.06900 m 4 3,200,000 µL 5 Determine the Significant Digits (Examples in Notebook)

  16. Math Operations with Significant Digits • When multiplying and/or dividing your answer must reflect the smallest number of significant digits.

  17. Math Operations with Significant Digits • When multiplying and/or dividing your answer must reflect the smallest number of significant digits. • (17.3 cm)(28 cm) = 484.4 cm2

  18. Math Operations with Significant Digits • When multiplying and/or dividing your answer must reflect the smallest number of significant digits. • (17.3 cm)(28 cm) = 484.4 cm2 = 480 cm2

  19. Math Operations with Significant Digits • When multiplying and/or dividing your answer must reflect the smallest number of significant digits. • (17.3 cm)(28 cm) = 484.4 cm2 = 480 cm2 • 708g ÷ 4.700ml = 150.63829 g/ml =

  20. Math Operations with Significant Digits • When multiplying and/or dividing your answer must reflect the smallest number of significant digits. • (17.3 cm)(28 cm) = 484.4 cm2 = 480 cm2 • 708g ÷ 4.700ml = 150.63829 g/ml = 151g/ml

  21. Addition and/or Subtraction reflects the fewest decimal placesdecimal places. • 24.6 cm − 17.01 cm = 7.59 cm

  22. Addition and/or Subtraction reflects the fewest decimal placesdecimal places. • 24.6 cm − 17.01 cm = 7.59 cm = 7.6 cm

  23. Addition and/or Subtraction reflects the fewest decimal placesdecimal places. • 24.6 cm − 17.01 cm = 7.59 cm = 7.6 cm • 8.5g + 1.32g + 0.18g =

  24. Addition and/or Subtraction reflects the fewest decimal placesdecimal places. • 24.6 cm − 17.01 cm = 7.59 cm = 7.6 cm • 8.5g + 1.32g + 0.18g = 10g

  25. Addition and/or Subtraction reflects the fewest decimal placesdecimal places. • 24.6 cm − 17.01 cm = 7.59 cm = 7.6 cm • 8.5g + 1.32g + 0.18g = 10g = 10.0g

  26. Homework • Worksheet – Significant Digits & Rounding.