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Using Numbers in Science

Using Numbers in Science. MEASUREMENT. quantitative observations not EXACT - there is always a smaller unit to consider measurements REQUIRE units (example: grams (g), centimeters (cm). EXAMPLE: measure height & width of paper. If the next number is 0-4 , round  .

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Using Numbers in Science

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  1. Using Numbers in Science

  2. MEASUREMENT • quantitative observations • not EXACT - there is always a smaller unit to consider • measurements REQUIRE units (example: grams (g), centimeters (cm)

  3. EXAMPLE: measure height & width of paper

  4. If the next number is 0-4, round . • If the next number is 5-8, round . • If the next number is 9, round up to the next tens place

  5. PRACTICE • Round 58.594 to the nearest tenth. • Round 9,331 to the nearest thousand. • Round 84.6 to the nearest ten. • Round .8491 to the nearest tenth. • Round .8491 to the nearest hundredth. • Round 751 to the nearest hundred. • Round 751 to the nearest ten.

  6. Rounding Answers • 58.594 to the nearest tenth = 58.6 • 9,331 to the nearest thousand = 9,000 • 84.6 to the nearest ten = 80.0 • .8491 to the nearest tenth = .8 • .8491 to the nearest hundredth = .85 • 751 to the nearest hundred = 800 • 751 to the nearest ten = 750

  7. AVERAGING • Scientists do repeated trials then average the results. • Add all the numbers, then divide by the number of trials. • In this class, get in the habit of rounding to a tenth unless otherwise directed.

  8. PRACTICE • Average the following figures: • 88.1 • 84.9 • 84.7 • 86.5 • 87.0

  9. Average = 86.24 Steps: a. 88.1 + 84.9 + 84.7 + 86.5 + 87.0 = 431.2 b. 431.2 ÷ 5 = 86.24 Bonus! Rounded to tenths place = 86.2

  10. PRACTICE • Round these figures to the nearest hundredth then average them. • 385.9326 • 391.8842 • 372.5291 • 382.9672 • 379.8006

  11. Test for following directions! • Round first, then average: • 385.9326 = 385.93 • 391.8842 = 391.88 • 372.5291 = 372.53 • 382.9672 = 382.97 • 379.8006 = 379.80 385.93 + 391.93 + 372.53 + 382.97 + 379.80 = 1913.16 1913.16 ÷ 5 = 382.632 √ for understanding: is 382.632 in between the highest and lowest number?

  12. PRACTICE • Average these figures then round them to the nearest tenth. • 46.93 • 51.37 • 49.44 • 50.21 • 47.96

  13. Read and Follow directions! • Average first, then round to the nearest tenth. 46.93 + 51.37 + 49.44 + 50.21 + 47.96 = 245.91 ÷ 5 = 49.182 49.182 = 49.2

  14. Accuracy in measurement describes how closely the measurement from your system matches the actual or true measurement of the thing being measured. It is the difference between the observed average of measurements and the true average. • Think of accuracy as the “trustworthiness” of a measurement system. • Precision in measurement describes how well a measurement system will  return the same measure; that is its Repeatability.

  15. Accuracy vs Precision

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