Ch. 1 lecture b
1. Scientific notation is used to write very large or small numbers and involves moving the decimal point so the first non-zero digit is to the left of the decimal, with the power of 10 indicating the number of places the decimal was moved. Units of measurement and prefixes are used to represent large and small quantities. 2. Equalities show equivalent measurements between units and can be used to derive conversion factors. The factor-label method involves setting up a ratio between the given and desired units, with the unit in the numerator cancelling the unit in the denominator to give the conversion in the desired unit. 3. Examples are provided for measuring temperatures on thermometers, converting between units like hours to minutes using conversion factors
Ch. 1 lecture b
- 1. 1/11/13 CHM 101 Chapter 1: Matter & Measurement Part B
- 2. Scientific Notation Scientific notation is used to write very large or very small numbers. A number in scientific notation contains a coefficient and a power of 10. coefficient power of ten coefficient power of ten 1.5 x 102 7.35 x 10-4 To write a number in scientific notation, the decimal point is moved so it will lie after the first digit. All significant figures are written. 52 000. = 5.2000 x 10 4 0.00378 = 3.78 x 10-3 4 spaces left 3 spaces right (use negative exponent) (use positive exponent) See Section 1.6 in your text for a detailed treatment of scientific notation (ASK FOR HELP!)
- 3. Units of Measurement You MUST know the prefixes below and be able to use them as conversion factors. Used to represent large quantities Used to represent small quantities
- 4. Equalities An equality states the same measurement in two different units, or in the same unit with two different prefixes. 1 km = 1 x 103 m 1 cm = 1 x 10-2 1 mg = 1 x 10-3 g 1 m = 1 x 10-3 km m 1 x 103 mg = 1 g 1 m = 100 cm 1000 m = 1 km 1000 mg = 1 g Equalities are also written for relationships between units of the metric system, U.S. units, or between metric and U.S. units. 1 in. = 2.54 cm 454 g = 1 lb
- 5. Conversion Factors A conversion factor is a fraction obtained from an equality. Equality: 1 in. = 2.54 cm The conversion factor is written as a ratio with a numerator and denominator. It can be inverted to give two conversion factors for every equality. 1 in. 2.54 cm or 2.54 cm 1 in. Equality: 1 m = 1 x 106 mm 1m 1×10 6 μm or 1×10 6 μm 1m
- 6. Factor-Label Method for Conversions How many minutes are 2.5 hours? Given unit = 2.5 hr Needed unit = min Unit Plan = hr min Setup problem to cancel hours (hr). Given Conversion Needed unit factor unit 2.5 hr x 60 min = 150 min (2 SF) 1 hr **Always write out the conversion factor with units. Cross through the units that cancel and make sure you end with the desired unit.
- 7. Factor-Label Method for Conversions How many minutes are 2.5 hours? Given unit = 2.5 hr Needed unit = min Unit Plan = hr min Setup problem to cancel hours (hr). Given Conversion Needed unit factor unit 2.5 hr x 60 min = 150 min (2 SF) 1 hr **Always write out the conversion factor with units. Cross through the units that cancel and make sure you end with the desired unit.
- 8. Units & Conversion Factors The diameter of an average sodium atom is 186 nm. What is the diameter in cm? In inches? A man weighs 83.95 kg. What is his weight in pounds? Do you know how to enter scientific notation on your calculator?
- 9. Record the temperatures on the thermometers below as accurately as possible. 28°C 28°C 27°C 27°C 26°C 26°C 25°C 25°C °C °C Always estimate one digit beyond the last marking.
- 10. Now Let’s Practice Measuring and Converting Units using the Factor-Label Method