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Measurement

Measurement. Scientific Notation. Way of expressing a value as the product of a number between 1 and 10 and a power of 10 Ex. 602,000,000,000,000 can be written 6.02x10 14. Significant Figures. Include digits that are known, plus a last digit that is estimated Rules:

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Measurement

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  1. Measurement

  2. Scientific Notation • Way of expressing a value as the product of a number between 1 and 10 and a power of 10 • Ex. 602,000,000,000,000 can be written 6.02x1014

  3. Significant Figures • Include digits that are known, plus a last digit that is estimated • Rules: • Every nonzero digit in a reported measurement is significant. Ex 24.7m, 0.743m, 714m • Zeros appearing inbetween of nonzero digits are significant. Ex. 7003m, 40.79m, 1.503m • Leftmost zeros appearing in front of nonzero digits are not significant. They are placeholders. Ex. 0.0071m, 0.42m, 0.000099m • You can eliminate placeholders by writing in scientific notation

  4. Significant Figures (cont) • Rules • Zeros at the end of a number and to the right of a decimal point are always significant. Ex. 43.00m, 1.010m, 9.000m • Zeros at the rightmost of a measurement that lie to the left of an understood decimal point are not significant if they serve as a placeholder. Ex. 300m, 7000 m, 27,210m • Use Scientific notation to show zeros are significant, Ex. 3.00x102

  5. Using Significant Figures in Calculations • Rounding • Decide on the amount of sig figs the answer should have • Round to that number counting to the left • If the number to the right of the last sig fig is less than 5 the number is dropped • If the digit is more than 5 then the last sig fig is rounded up by 1

  6. Sig Fig Calculations (cont) • Addition and Subtraction • Should be rounded to the same number of decimal places as the measurement with the least number of decimal places • Multiplication and Division • Round the answer to the same number of sig figs as the measurement with the least number of sig figs

  7. Precision and Accuracy • Precision- gauge of how exact a measurement is. • The more sig figs a measurement has the more precise it is • Accuracy- closeness of a measurement to the actual value of what is being measured Precision Accuracy

  8. The Metric System • The metric system is a measurement system based on our decimal (base 10) number system. • Other countries and all scientists and engineers use the metric system for measurement.

  9. Metric Prefixes • Metric Units • The metric system has prefix modifiers that are multiples of 10.

  10. Place Values of Metric Prefixes

  11. Meters • Meters measure length or distance • One millimeter is about the thickness of a dime.

  12. Meters • One centimeter is about the width of a large paper clip • or your fingernail.

  13. Meters • A meter is about the width of a doorway

  14. Meters • A kilometer is about six city blocks or 10 football fields. • 1.6 kilometers is about 1 mile

  15. Gram • Grams are used to measure mass or the weight of an object.

  16. Grams • A milligram weighs about as much as a grain of salt.

  17. Grams • 1 gram weighs about as much as a small paper clip. • 1 kilogram weighs about as much as 6 apples or 2 pounds.

  18. Liters • Liters measure liquids or capacity. 2 Liter Soda

  19. Liter • 1 milliliter is about the amount of one drop

  20. Liter • 1 liter is half of a 2 liter bottle of Coke or other soda

  21. Liter • A kiloliter would be about 500 2-liter bottles of pop

  22. Changing Metric Units • To change from one unit to another in the metric system you simply multiply or divide by a power of 10.

  23. To change from a larger unit to a smaller unit, you need to multiply. 1 km x 1000 = 1000 m 1 m x 100 = 100 cm 1 cm x 10 = 10mm

  24. Place Values of Metric Prefixes Movethe decimal point to the right to multiply.

  25. To change from smaller units to larger units you divide by a power of ten. 1000mm ÷ 10 = 100cm 100cm ÷ 10 = 10dm 10dm ÷ 10 = 1m

  26. Place Values of Metric Prefixes Movethe decimal point to the left to divide.

  27. Temperature Properties • Measure of how hot or cold an object is • When 2 objects are close heat will transfer from the hotter object to the cooler object • When temperature increases substances will expand. • When temperature decreases substances will contract

  28. Measuring Temperature in Fahrenheit • Symbol for Fahrenheit is °F • Freezing point of water is 32°F • Boiling point of water is 212°F

  29. Measuring Temperature in Celsius • Symbol for Celsius is °C • Freezing point of water is 0 °C • Boiling point of water is 100 °C

  30. Measuring Temperature in Kelvin • Symbol for Kelvin is K • Freezing point of water is 273 K • Boiling point of water is 373 K

  31. Converting Fahrenheit and Celsius • °C = 5/9 (°F-32.0°) • °F = 9/5 (°C) + 32.0°

  32. Converting Celsius and Kelvin • K= °C +273 • °C = K – 273

  33. Conversions

  34. Conversion • Conversion factors are a way to express the one quantity in different ways • Ex. 1 dollar = 4 quarters= 10 dimes= 20 nickels =100 pennies • Ex. 1 meter= 10 decimeters= 100 centimeters = 1000 millimeters

  35. Conversion Factors • Ratio of equivalent measurements • 2 dollars = 20 dimes = 1 2 dollars 2 dollars • 1 meter = 100 centimeters = 1 1 meter 1 meter

  36. Example • How many seconds are in a workday that lasts exactly eight hours?

  37. Example • What is 0.073cm in micrometers?

  38. Example • The mass per unit volume of a substance in a property called density. The density of manganese, a metallic element, is 7.21 g/cm3. What is the density of manganese expressed in units kg/m3?

  39. Density

  40. Determining Density • Ratio of the mass of an object to is volume • Density = mass/volume • Density depends on what the substance is made of not how much of the substance you have • Ex 10.0 cm3 piece of lead has a mass of 114 g. What is the density?

  41. Density and Temperature • As temperature increases, the volume of a substance increases • Since volume increases, then the density will decrease as the temperature increases

  42. Calculating volume and mass from density • Volume = mass/density • Mass = density X volume

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