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Understanding Significant Figures, Measurement, and Density Calculations

This guide covers the essentials of significant figures and measurement in mathematics, including identification of significant zeros, rules for adding and subtracting decimals, and guidelines for multiplication and division concerning significant figures. It also introduces the metric system conversion, density calculations, and methods of density by displacement. Key concepts such as accuracy vs. precision and percent error are explained to ensure a fundamental understanding of how to record measurements and calculate physical properties effectively.

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Understanding Significant Figures, Measurement, and Density Calculations

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Presentation Transcript

  1. Math and Measurement

  2. Significant Figures Significant Zeros • Leading zeros are never significant • Trailing zeros only count if there’s a decimal point somewhere in the number Examples 4002 200 200. 0.0020 2.00 x 102

  3. Math with Significant Figures Adding and subtracting (think DECIMALS) • 2.55 + 5.106 = 7.66 Multiplying and dividing (think total SIGFIGS) • 0.50 X 2.00 = 1.0 10.00 - 5.5 = 3.00  1.500 =

  4. Recording Measurement • Estimate the last digit What is the measurement?

  5. The Metric System 1 K= 1000  100 c = 1  1000 m = 1  Where  = g, L, m, s How many kJ in 4,320 J?

  6. Density Density = mass/volume What is the mass of 2.0 L of gas with a density of 2.0 g/L? m V D

  7. Density by Displacement • Density by displacement • Measure the mass of an object in grams. • Add known amount of water to a graduated cylinder and record the volume in mL. • Add the object to the water and measure the new volume in mL. • Density = mass/volume

  8. Accurate, not precise Precise, not accurate Precise and accurate Not precise, not accurate Accuracy vs Precision

  9. Accuracy vs Precision How close the value is to the true value How close the values are to each other. Percent Error = x 100

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