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Measurement

Measurement. Exact Measurements. Where the values are known without any estimation. Examples of Exact Numbers. exactly 17 students in this class exactly 12 eggs in a dozen exactly 1000 g in a kilogram exactly 2.54 cm in an inch

kennedy-howe
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Measurement

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  1. Measurement

  2. Exact Measurements Where the values are known without any estimation.

  3. Examples of Exact Numbers • exactly 17 students in this class • exactly 12 eggs in a dozen • exactly 1000 g in a kilogram • exactly 2.54 cm in an inch • The number 1 in any conversion factor between units, as in 1 m = 100 cm is an exact number

  4. Inexact Measurements Values where some estimation is used to calculate. There is some uncertainty.

  5. Examples of Inexact Numbers • Height • Weight • Length • Width Any number obtained by measurement is always inexact.

  6. Equipment Error Inherent limitations in the equipment used to measure quantities

  7. Human Error Differences in how different people make the same measurement

  8. Remember!!! Uncertainties always exist in measured quantities!!!

  9. What To Do, What To Do???

  10. Search for Significance! Use significant digits to indicate the accuracy of the measurement.

  11. Significant Figures When making measurements, it is the size of the measurement needed to be precise.

  12. Sig. Fig. Rule • Non-zero numbers are always significant • Zeros between non-zero numbers are always significant. • All final zeros to the right of the decimal place are significant.

  13. Sig. Fig. Rule • Zeros that act as placeholders are not significant. • All numbers in calculations should have same sig. fig. go with the smallest sig. fig. number • Counting numbers and defined constants do not change.

  14. 857 950 1800 45.2 45.0 92000.0 3 2 2 3 3 6 What’s the Sig. Fig. • 0.00243 • 505 • 0.0012300 • 3.22X105 • 1200.0060 • 0023 • 3 • 3 • 5 • 3 • 8 • 2

  15. Scientific Notation Expresses numbers as a multiple of two factors-a number between 1 and 10, and 10 raised to a power or exponent; makes it easier to write a really big number or really small number.

  16. 15624 17853 19278 17750 17650 24503 276453 15600 17900 19300 17800 17600 24500 276000 Round to 3 sig. fig.

  17. Rounding Rules • If digit after sig # is above 5, then round up • If digit after sig # is below 5 then leave as is • If digit after sig # is 5 and # after 5 is not zero, then round up • If digit after sig # is 5 and # after 5 is zero; if sig # is odd round up and if even then leave as is.

  18. Accuracy and Precision

  19. Precision Is the degree of exactness to which the measurement of a quantity can be reproduced

  20. Accuracy Is the extent to which a measured value agrees with the standard value of a quantity.

  21. Precision and Accuracy

  22. Percent Error

  23. Scale A determined measurement with a distinct base line.

  24. 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 101 deka da 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro µ 10-9 nano n 10-12 pico p 10-15 femto f 10-18 atto a

  25. Dimensional Analysis A problem solving method that focuses on the units that are used to describe matter.

  26. System International Units (SI Units) Units are a name tag that lets you know what measurement the number is for. The SI Units are the standard units use throughout the world.

  27. Time= second (s) Length= meter (m) Mass= kilogram (kg) Temperature= Kelvin (K) Volume= liter (L) or cubic centimeter (cm3) Density= g/cm3 SI Units

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