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Understanding Measurement: Accuracy and Precision

Learn about different types of measurements, significant figures, rules for determining which zeros are significant, and how to round calculations accurately. Boost your scientific measurement skills now!

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Understanding Measurement: Accuracy and Precision

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  1. Scientific measurement

  2. Types of measurement • Quantitative- use numbers to describe • Qualitative- use description without numbers • 4 feet • extra large • Hot • 100ºF

  3. How good are the measurements? • Scientists use two words to describe how good the measurements are • Accuracy- how close the measurement is to the actual value • Precision- how well can the measurement be repeated

  4. Differences • Accuracy can be true of an individual measurement or the average of several • Precision requires several measurements before anything can be said about it • examples

  5. Let’s use a golf anaolgy

  6. Accurate? No Precise? Yes

  7. Accurate? Yes Precise? Yes

  8. Precise? No Accurate? No

  9. Accurate? Yes Precise? We cant say!

  10. 1. Significant Figures 2.35 cm • Indicate precision of a measurement. • Recording Sig Figs • Sig figs in a measurement include the known digits plus a final estimated digit

  11. 2. NON-ZEROs - significant 2.35 cm All NON-Zeros are SIGNIFICANT • 1, 2, 3, 4, 5, 6, 7, 8, & 9 • There are ____Sig figs in the measurement below? Answer?= 3

  12. Rules for determining which ZEROs are significant 3. “SANDWICHED” zeros - significant • Zeros between other nonzero(1,2,3…) digits are significant • 50.3 has three sig fig • 3.0025 has five sig fig

  13. Rules for determining which ZEROs are significant 4. “BEGINNING” Zeros – not significant • Zeros in front of the 1st nonzero digit are NOT significant • 0.892 has three sig fig • 0.0008 has one sig fig

  14. Rules for determining which ZEROs are significant 5. ENDING zeros – significant or not significant? • Ending zeros in a number without a decimal - not significant • 1000 has one sig fig • Ending zeros in a number with a decimal - significant • 57.00 has four sig fig • 2.000000 has seven sig fig • 56700. has five sig fig

  15. Sig Figs • Only measurements have sig figs. • Counted numbers are exact • A dozen is exactly 12 • A a piece of paper is measured 11 inches tall. • Being able to locate, and count significant figures is an important skill.

  16. Sig figs. How many sig figs in the following measurements? • 458 g • 4085 g • 4850 g • 0.0485 g • 0.004085 g • 40.004085 g

  17. Sig Figs. • 405.0 g • 4050 g • 0.450 g • 4050.05 g • 0.0500060 g • Next we learn the rules for calculations

  18. 6. Add/Subtract – 3.75 + 4.1_ 7.85 3.75 + 4.1 7.85 224 + 130 354 224 + 130 354  7.9  350 • The final answer should be rounded to have the same number of decimal places as the measurement with the smallest number of decimal places.

  19. 6. Multiply/Divide – 3 SF (13.91)(23.3) = 324.103 4 SF 3 SF 324 • The final answer has the same number of significant figures as the measurement having the least number of sig figures.

  20. 7.Rounding? No decimal places no decimal places 2 decimal places 213.67 - 98 = 115.67 Calculator answer 116 round up Check addition Rule (least # of decimal places), then round • Always reduce to significance by Rounding when you’ve finished and reached the end of the whole problem.

  21. 7.Rounding? 3 sf 7.32(8.189) = 59.94348 Calculator answer 3sf 4sf 59.9 rounded down Check multiple rule (least # of sigfig), then round • Always reduce to significance by Rounding when you’ve finished and reached the end of the whole problem.

  22. Rounding rules • look at the number behind the one you’re rounding. • If it is 0 to 4 don’t change it • If it is 5 to 9 make it one bigger • round 45.462 to four sig figs • to three sig figs • to two sig figs • to one sig fig

  23. Practice • 4.8 + 6.8765 • 520 + 94.98 • 0.0045 + 2.113 • 6.0 x 102 - 3.8 x 103 • 5.4 - 3.28 • 6.7 - .542 • 500 -126 • 6.0 x 10-2 - 3.8 x 10-3

  24. Multiplication and Division • 4.5 / 6.245 • 4.5 x 6.245 • 9.8764 x .043 • 3.876 / 1983 • 16547 / 714

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