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Measurements and Conversions

Measurements and Conversions. Why Measure?. Measurements give specific information Different types: - Base Units: System International Units (or Metric) Standard for many scientific measurements - Derived Units Combinations of base units Ex: density or volume. Metric Units

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Measurements and Conversions

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  1. Measurements and Conversions

  2. Why Measure? • Measurements give specific information • Different types: - Base Units: System International Units (or Metric) • Standard for many scientific measurements - Derived Units • Combinations of base units • Ex: density or volume

  3. Metric Units Mass – the amount of matter in an object, grams (g) Volume – the amount of space an object occupies, liter (L) Length – distance between two points, meter (m)

  4. Metric Prefixes

  5. Converting with metric units • K H D __ d c m • Place 1 under starting prefix • Place 2 under ending prefix • Draw an arrow from 1 to 2. This is the direction to move the decimal point. • Count the number of places to go from 1 to 2. Be sure to count the __ space. • Move decimal point and rewrite number.

  6. Make the following metric conversions 13.5 g  ___ kg 2.75 mL  ___ L 150 mm  ___cm0.0150 m  ___cm 0.195 cg  ___ mg 0.750 L  ___mL 2.46 mg ___ kg 5.79 HL  ___ L 7.53 km  ___cm0.0432 g  ___mg 4150 cL ___ L 739 dm  ___ m 81.8 cg  ___kg418.2 m  ___ km

  7. Scientific Notation – a way of showing very large or small numbers. • 4.7 x 103 4.7 E 3 4.7 exp3 • 4.7 x 10 x 10 x 10 = 4,700 • Only significant numbers remain • The “number out front” is only allowed to have one nonzero digit to the left of the decimal point.

  8. Converting TO Scientific Notation • Place the decimal after the first digit • Count from the original decimal place to the new location. • That number will become the exponent. • If you counted: • To the left (starting # > 1) then + exponent • To the right (starting #< 1) then - exponent • Write “new” number x 10exponent • Do not write any placeholding zeros • Non-significant numbers

  9. Converting FROM Scientific Notation • The exponent or power tells how many places the decimal point will be moved. • If the exponent is positive, the decimal point moves to the right. - The number will be > 1 • If the exponent is negative, the decimal point moves to the left. - The number will be < 1

  10. Warm-Up • Convert the following: 1. 41,300 L to kL 2. 13,200 kg to g 3. 72 cm to mm • 41.3 kL • 13,200,000g • 720mm

  11. Warm-Up • Express is Scientific Notation: • 1600 • 0.0053 • 134.8 1. 1.6 x 103 2. 5.3 x 10-3 3. 1.348 x 102

  12. Reliability of Measurements • Exact numbers - counting numbers - Not measurements - A stated value that is certain • Example: 100 years = 1 century, 1 foot = 12 inches • Measured numbers- have uncertainty because of the equipment/device used and the observer

  13. Accuracy and Precision • Accuracy - How close the measured value is to the accepted value • Precision - How close a series of measurements are to each other

  14. Significant Figures • Scientists use significant figures to show how precisely an experiment was performed • Significant Figures (sig figs) – all known digits in a measurement plus one estimated digit. • Scientists use rules to determine the number of significant figures in a particular value

  15. When to use Sig Fig • When something is MEASURED • Not when something is COUNTED

  16. Coast to Coast Sig Figs Atlantic/Pacific Rule: • If a decimal point is absent, count from the Atlantic (right) side starting with the first nonzero digit. • If a decimal point is present, count from the Pacific (left) side starting with the first nonzero digit

  17. Coast to Coast practice • 47.08020 • 10 • 5400600 • 1.158 • 0.007013 • 100.

  18. Rounding numbers in calculations • Add/subtract: the answer will have the same number of places past the decimal point as the measurement with the fewest places past the decimal point. • Multiply/divide: the answer will have the same number of sig figs as the measurement with the fewest number of sig figs. • Rounding off numbers: 0-4 drop, 5-9 add 1 • Defined or exact numbers have an infinite number of significant figures.

  19. WHEN to round off significant figures • When the rules for rounding change • i.e. going from addition  division or multiplication  addition • At the end of the problem, and you are giving the final answer

  20. Conversions that you are responsible for knowing… • 12 in = 1 ft • 3 ft = 1 yd • 5280 ft = 1 mile • 60 sec = 1 min • 60 min = 1 hr • 24 hr = 1 day • 7 day = 1 wk • 365.25 days = 1 yr • 16 oz = 1 lb • 2000 lb = 1 ton • 8 oz = 1 cup • 2 cups = 1 pint • 2 pints = 1 quart • 4 quarts = 1 gallon

  21. Unit Analysis/Dimensional Analysis • A method of converting from 1 set of units to another set of units using a series of conversion factors. • A conversion factor is a fraction made from the two parts of the equivalency. • 12 in. = 1 ft • Each equivalency can produce two conversion factors.

  22. Convert 22 inches to feet • List possible conversion factors: • Set up grid with starting number and units in the upper left side • Plug in conversions so that the same units are on the diagonal

  23. Unit Analysis Practice • 5.75 min  months • 135 km  cm • 17.5 oz  gal • 1.5 mile  inch • 145 mg  hg • 135 mL  L

  24. 5.75 min  month • 5.75 min_ 1 hr 1 day 1 yr 12 mos= 1.31 x 104 months • 60 min 24 hr 365.25 day 1 yr • 135 km  cm • 135 km 1000 m 1 cm = 13,500,000 cm • 1 km 0.01 m • 17.5 oz  gal • 17.5 oz 1 qt 1 gal = 0.138 gal • 32 oz4 qt • 1.5 mile  inch • 1.5 mile 5280 ft 12 in = 95,000 in • 1 mile 1 ft

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