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4 Stating a Measurement In a measurement, a number is followed by a unit. Observe the following examples of measurements: Number Unit 35 m 0.25 L 225 kg 3.4 hr
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5 The Metric System (SI) The metric system or SI (international system) is
6 Units in the Metric System In the metric (SI) system, one unit is used for each type of measurement: Measurement Metric SI length meter (m) meter (m) volume liter (L) cubic meter (m3) mass gram (g) kilogram (kg) time second (s) second (s) temperature Celsius (C) Kelvin (K)
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11 For each of the following, indicate whether the unit describes 1) length, 2) mass, or 3) volume. ____ A. A bag of onions has a mass of 2.6 kg. ____ B. A person is 2.0 m tall. ____ C. A medication contains 0.50 g aspirin. ____ D. A bottle contains 1.5 L of water. Learning Check
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12 For each of the following, indicate whether the unit describes 1) length, 2) mass, or 3) volume. 2 A. A bag of onions has a mass of 2.6 kg. 1 B. A person is 2.0 m tall. 2 C. A medication contains 0.50 g aspirin. 3 D. A bottle contains 1.5 L of water. Solution
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13 Learning Check Identify the measurement with an SI unit. A. John’s height is 1) 1.5 yd 2) 6 ft 3) 2.1 m B. The race was won in 1) 19.6 s 2) 14.2 min 3) 3.5 hr C. The mass of a lemon is 1) 12 oz 2) 0.145 kg 3) 0.6 lb D. The temperature is 1) 85C 2) 255 K 3) 45F
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14 Solution Identify the measurement with an SI unit. A. John’s height is 3) 2.1 m B. The race was won in 1) 19.6 s C. The mass of a lemon is 2) 0.145 kg D. The temperature is 2) 255 K
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15 STEP 1 State the given and needed units. STEP 2 Write a plan to convert the given unit to the needed unit. STEP 3 Write equalities/conversion factors that connect the units. STEP 4 Set up problem with factors to cancel units and calculate the answer. Unit 1 x Unit 2 = Unit 2 Unit 1 Given Conversion Needed unit factor unit Guide to Problem Solving (GPS)
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17 A rattlesnake is 2.44 m long. How long is the snake in centimeters? 1) 2440 cm 2) 244 cm 3) 24.4 cm Learning Check
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18 A rattlesnake is 2.44 m long. How long is the snake in centimeters? 2) 244 cm given conversion needed unit factor unit 2.44 m x 100 cm = 244 cm 1 m Solution
Often, two or more conversion factors are required to obtain the unit needed for the answer.
Unit 1 Unit 2 Unit 3
Additional conversion factors can be placed in the setup to cancel each preceding unit
Given unit x factor 1 x factor 2 = needed unit Unit 1 x Unit 2 x Unit 3 = Unit 3 Unit 1 Unit 2 Using Two or More Factors
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20 How many minutes are in 1.4 days? Given unit: 1.4 days Needed unit: min Plan: days hr min Equalties: 1 day = 24 hr 1 hr = 60 min Set up problem: 1.4 days x 24 hr x 60 min = 2.0 x 103 min 1 day 1 hr Example: Problem Solving
Be sure to check your unit cancellation in the setup.
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The units in the conversion factors must cancel to give the correct unit for the answer.
What is wrong with the following setup?1.4 day x 1 day x 1 hr 24 hr 60 min Units = day2/min is Not the needed unit Units don’t cancel properly. Check the Unit Cancellation
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More units Area m2 = m x m Volume m3 = m x m x m Density mass/volume g/mL or Kg/L 22
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K = oC + 273 Ex 23 oC = _______ K 135 K = ________ oC 1L = 1 dm3 1 m3 =1000L Ex 27 m3 = ________ L 23
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24 Osmium is a very dense metal. What is its density in g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3? 1) 2.25 g/cm3 2) 22.5 g/cm3 3) 111 g/cm3 Learning Check
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25 Given: mass = 50.0 g volume = 2.22 cm3 Plan: Write the density expression. D = mass volume Express mass in grams and volume in cm3mass = 50.0 g volume = 2.22 cm3 Set up problem using mass and volume. D = 50.0 g = 22.522522 g/cm3 2.22 cm3 = 22.5 g/cm3 Solution
Ice floats in water because the density of ice is less than the density of water.
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Aluminum sinks because its density is greater than the density of water.
29 Which diagram correctly represents the liquid layers in the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL,) water (W) (1.0 g/mL) 1 2 3 K W V V W K W V K Learning Check
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30 1) vegetable oil 0.91 g/mL water 1.0 g/mL Karo syrup 1.4 g/mL V W K Solution
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35 Comparing Numbers in Standard and Scientific Notation Number in Standard Format Scientific Notation Diameter of the Earth 12 800 000 m 1.28 x 107 m Mass of a human 68 kg 6.8 x 101 kg Mass of a hummingbird 0.002 kg 2 x 10-3 kg Length of a pox virus 0.000 000 3 cm 3 x 10-7 cm
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36 Learning Check Select the correct scientific notation for each. A. 0.000 008 1) 8 x 106 2) 8 x 10-6 3) 0.8 x 10-5 B. 72 000 1) 7.2 x 104 2) 72 x 103 3) 7.2 x 10-4
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37 Solution Select the correct scientific notation for each. A. 0.000 008 2) 8 x 10-6 B. 72 000 1) 7.2 x 104
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38 Learning Check Write each as a standard number. A. 2.0 x 10-2 1) 200 2) 0.00203) 0.020 B. 1.8 x 105 1) 180 000 2) 0.000 0183) 18 000
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39 Solution Write each as a standard number. A. 2.0 x 10-2 3) 0.020 B. 1.8 x 105 1) 180 000
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