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Measurements and Calculations

Learn about SI units, scientific notation, significant figures, density calculations, and unit conversions in this guide. Understand how to measure accurately and calculate percent error.

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Measurements and Calculations

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  1. Measurements and Calculations Chapter 2

  2. Units of Measurement • Measurements involve NUMBER and UNIT • Represent a quantity: has magnitude, size, or amount • Gram = unit of measurement • Mass = quantity

  3. Units of Measurement • Scientists around the world agree on one system… • International System of Units (le Systeme International d’Unites) • SI units • Built from seven base units

  4. SI Base Units

  5. Units of Measurement

  6. Units of Measurement • Metric Prefixes – make units easier to use • Make the unit smaller or larger • Unit = prefix + base unit

  7. Mass • Measures quantity of matter • SI unit: kilogram, kg • 1kg = 1000 g • gram used for smaller masses • Weight: measure of gravitational pull

  8. Length • SI unit: meter, m • Longer distances: kilometer, km • 1km = 1000 m • Shorter distances: centimeter, cm • 1 m = 100 cm

  9. Volume Volume is the amount of space an object occupies. It is a derived unit: combination of base units by multiplying or dividing SI unit is m 3 Volume: l x w x h = m x m x m = m3 • Also: liters (L), mL, dm3 and cm3 • 1 L = 1 dm3 = 1000mL = 1000 cm3

  10. Derived Units

  11. Scientific Notation • Put the numbers in the form N x 10n • N has one # to left of decimal • If # is bigger than 1  + exponent • If # is less than 1  - exponent

  12. Scientific Notation • Review: Write in scientific notation 32,700 0.0003412 3.901 x 10-6 4.755 x 108

  13. 1 2 3 4 5 Significant Figures (sig figs) • How many numbers mean anything? • When we measure, we can (and do) always estimate between the smallest marks.

  14. Significant figures (sig figs) • Better marks means a better estimate. • Last number measured actually an estimate 1 2 3 4 5

  15. Sig Figs • They needed a set of rules to decide which numbers are significant • Only measurements have sig figs. • Counted numbers are exact : A dozen is exactly 12 Conversion factors: 100 cm = 1 m

  16. Unique problem • 50 has only 1 significant figure • if it really has two, how can I write it? • Scientific notation • 5.0 x 1012 sig figs • Scientific Notation shows ALL sig figs

  17. Rounding rules • Round 454.62 to four sig figs • to three sig figs • to two sig figs • to one sig fig

  18. Density

  19. Density • Density = mass D = m volume V • Units: g/cm3 or g/mL but SI unitis kg/m3 • derived unit • Used to identify substances • Varies with temperature • As temp. increases density…???

  20. Density

  21. Density Examples • If a metal block has a mass of 65.0 grams and a volume of 22 cubic centimeters, what is the density of the block? • D = m V • D = 65.0 g = 3.0 g/cm3 22 cm3

  22. Density Examples • Aluminum has a density of 2.7 g/cm3. What volume of aluminum has a mass of 60 grams? • D = M V 20 cm3

  23. Density Examples • Gold has a density of 19.3 g/cm3. A block of metal has a mass of 80 g and a volume of 12 cm3. Could this block be a piece of gold? • No, because this block has a density of 7 g/cm3s

  24. Unit Conversions

  25. Unit Conversions Given information in one unit  need to to convert it to another unit ! • Identify what’s given • Organize plan of attack • Carry out plan WITH UNITS!!

  26. Conversion factors • “A ratio of equivalent measurements.” • Start with two things that are the same. 1 m = 100 cm • Does NOT change the VALUE, it changes the UNITS.

  27. Let’s Try Some! • 323 mm = _____ m • 3.2 miles = _____ in • 250 gallons= _______ml • 15 days = _______ min • 54.3cm3 = _____ m3 • 7.54ft2 = _______ in2

  28. Where do these measurements come from?

  29. Making Good Measurements • We can do 2 things: • Repeat measurement many times - reliable measurements get the same number over and over - this is precise

  30. 2. Test our measurement against a “standard”, or accepted value - measurement close to accepted value is accurate

  31. Measurements are Uncertain • Measuring instruments are never perfect • Skill of measurer • Measuring conditions • Measuring always involves estimation • Flickering # on balance • Between marks on instrument

  32. Calculating Percent Error (TableT) • Compares your measurement to accepted value • Negativeif measurement is too small • Positiveif measurement is too big

  33. Calculating Percent Error What is the % error for a mass measurement of 17.7g, given that the correct value is 21.2g?

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