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Measurements Scientific Notation Significant Figures

Measurements Scientific Notation Significant Figures. SI System. 1795 French scientists adopt system of standard units called the metric system . In 1960 the metric system was revised to the SI system. Systeme Internationale d’Unites Base Units Time – second Length – meter Mass - kilogram.

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Measurements Scientific Notation Significant Figures

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  1. MeasurementsScientific NotationSignificant Figures

  2. SI System • 1795 French scientists adopt system of standard units called the metric system. • In 1960 the metric system was revised to the SI system. • SystemeInternationaled’Unites • Base Units • Time – second • Length – meter • Mass - kilogram

  3. Base Units • Defined unit in a system of measurement that is based on an object or event in the physical world. • Independent of other units.

  4. Base Units

  5. Derived Units • Unit that is defined by a combination of base units. • Volume – the space occupied by an object. • derived unit – m3 • cm3 = mL • Density – ratio that compares mass of an object to its volume.

  6. Density • How can we rearrange this equation if we have the density and volume.

  7. Temperature • Kelvin scale, founded by William Thompson who was known as Lord Kelvin. • Water freezes at 273 K • It boils at 373K • The scale is the same as Celsius, just different temperature points • Celsius + 273 = Kelvin • Kelvin – 273 = Celsius

  8. Problems • If the density of an object is 2.70 g/cm3 and the mass of the object is 1.65g, what is the volume of the sample?

  9. Problem • Convert the following: • 357oC to Kelvin • 357oC + 273 = 630K • -39oC to Kelvin • -39oC + 273 = 234K • 266K to Celsius • 266K – 273 = -7oC • 332K to Celsius • 332K – 273 = 59oC

  10. Graphs • A visual display of data. • Circle Graphs or Pie Charts • Show parts of a fixed whole • Usually broken into % • Bar Graphs • Show how quantities vary • Measured quantity on y-axis • Independent variable on x-axis

  11. Graphs • Line Graphs • Most common in chemistry • Independent variable on x-axis • Dependent variable on y-axis • Can determine slope of line

  12. Prefixes • SI Prefixes mega (M)106 kilo (k) 103 basic unit deci (d) 10-1 centi (c) 10-2 milli (m) 10-3 micro (µ) 10-6 nano (n) 10-9 pico (p) 10-12

  13. Scientific Notation • Expresses numbers as a multiple of two factors: • A number between 1 and 10. • Ten raised to a power or exponent. • Exponent tells you how many times the first factor must be multiplied by 10. • A number larger than 1 expressed in scientific notation, the power of 10 is positive. • A number smaller than 1 has a negative power of 10.

  14. Problems • Express the following in scientific notation • Put the following scientific notation numbers in standard notation.

  15. Multiplying and Dividing with Scientific Notation • When multiplying terms in scientific notation, you multiply the coefficients, keep your base of 10 and add the exponents. • When dividing terms in scientific notation, you divide the coefficients, keep your base of 10 and subtract the exponents.

  16. Multiplying and Dividing

  17. Addition and Subtraction with Scientific Notation • When adding or subtracting in scientific notation: • Get terms to have the same exponent. • Add or subtract the coefficients. • Keep your base of ten. • Keep the exponent that both terms contained.

  18. Adding and Subtracting

  19. Significant Figures • Indicate the uncertainty of a measurement. • Include all known digits plus one estimated digit.

  20. Rules for Significant Figures (Digits) • All non-zero digits are significant. • 127.34 • Contains 5 significant digits. • All zeros between two non-zero digits are significant. • 120.007 • Contains 6 significant digits. • Unless specifically indicated by the context to be significant, ALL zeros to the left of an understood decimal point, but to the left of a non-zero digit are NOT significant. • 109,000 • Contains 3 significant digits

  21. Rules continued… • All zeros to the left of an expressed decimal point and to the right of a non-zero digit ARE significant. • 109,000. • Contains 6 significant figures. • All zeros to the right of a decimal point, but to the left of a non-zero digit are NOT significant. • 0.00476 • Contains 3 significant figures. • The single zero conventionally placed to the left of the decimal point is NEVER significant

  22. Rules continued… • ALL zeros to the right of the decimal point and to the right of a nonzero digit ARE significant. • 0.04060 • 30.00 • Both contain 4 significant digits. • Counting numbers and defined constants have an infinite number of significant digits. • 60 s = 1 min • 11 soccer players

  23. Operations with Significant Figures • Multiplication and Division • The answer contains the same number of significant figures as the measurement with the least amount of significant figures. • Addition and Subtraction • The answer has the same number of decimal places as the measurement with the least amount of decimal places.

  24. Precision vs. Accuracy • Precision • The agreement between measurements. • How close a set of measurements are to each other. • Accuracy • The nearness of a measurement to its actual value. • How close you are to the true value.

  25. Precision vs. Accuracy

  26. These thermometers have different levels of precision. The increments on the left are 0.2, but the ones on the right are 1.0. How should their temperatures be recorded? 37.53 5.8

  27. Percent Error • The ratio of an error to an accepted value.

  28. Example • You analyze a sample of copper sulfate and find that it is 68% copper. The theoretical value of copper is 80%. What is the percent error?

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