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Measurement

Measurement. 1. 2. 3. 4. 5. Significant figures (sig figs). How many numbers mean something When we measure something, we can (and do) always estimate between the smallest marks. Significant figures (sig figs). The better marks the better we can estimate.

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Measurement

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  1. Measurement

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

  3. Significant figures (sig figs) • The better marks the better we can estimate. • Scientist always understand that the last number recorded is actually an estimate 1 2 3 4 5

  4. Which numbers count? • All nonzero numbers in a recorded measurement are significant • Zeros between nonzeros are significant • 12004 • Zeros in front of nonzeros are NOT significant • 0.045

  5. Which numbers count? • zeros at the end of a number after the decimal point are significant • 45.8300 • Zeros after the number but no decimal are NOT significant • 458300

  6. Sig Figs • Only measurements have sig figs. • Counted numbers are exact • A dozen is exactly 12 • There are 2405 students in this school • Being able to locate, and count significant figures is an important skill.

  7. Sig Figs • How many sig figs in the following measurements? • 458 g • 4085 g • 4850 g • 0.0485 g • 0.004085 g • 40.004085 g

  8. Sig Figs • 405.0 g • 4050 g • 0.450 g • 4050.05 g • 0.0500060 g

  9. Problems • 50 is only 1 significant figure • if it really has two numbers, then how can I write it? • Scientific notation • 5.0 x 101 • now the zero counts.

  10. Multiplication and Division • Rule is simpler • Same number of sig figs in the answer as the least in the question • 3.6 x 653 = 2350.8 • With sf: 2400

  11. Multiplication and Division • Same rules for division Practice • 4.5 / 6.245 • 4.5 x 6.245 • 9.8764 x .043 • 3.876 / 1983 • 16547 / 714

  12. The Metric System An easy way to measure

  13. Measuring • The numbers are only HALF of a measurement “It is 10 long” • 10 what? • Numbers without units are meaningless!

  14. The Metric System • Easier to use because it is a decimal system • Every conversion is by some power of 10. • A metric unit has two parts: A prefix and a base unit. • prefix tells you how many times to divide or multiply by 10.

  15. Base Units • Length - meter more than a yard - m • Mass - grams - about a raisin - g • Time - second - s • Temperature - Kelvin or ºCelsius K or C • Energy – Joules - J • Volume - Liter - half a two liter bottle- L • Amount of substance - mole - mol

  16. Prefixes • kilo k 1000 • deci d 1/10 • centi c 1/100 • milli m 1/1000 • kilometer - about 0.6 miles • centimeter - less than half an inch • millimeter - a paperclip wire

  17. k h D d c m Converting in Metric • how far you have to move on this chart tells you how far and which direction to move the decimal place. • The box is the base unit: meters, Liters, grams, etc.

  18. k h D d c m Conversions • convert 25 mg to grams • convert 0.45 km to mm • convert 35 mL to liters • It works because the math works, we are dividing or multiplying by 10 the correct number of times

  19. Converting from metric to standard • Requires conversion factors • Use dimensional analysis • Units must work out in the final answer

  20. Dimensional Analysis • A ruler is 12.0 inches long. How long is it in cm? ( 1 inch is 2.54 cm) • in meters? • A race is 10.0 km long. How far is this in miles? • 1 mile = 5280ft • 1 meter = 3.281 ft • Pikes peak is 14,110 ft above sea level. What is this in meters?

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