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• 1.4 Problem Solving in Chemistry > 1 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Chapter 1 Introduction to Chemistry 1.1 The Scope of Chemistry 1.2 Chemistry and You 1.3 Thinking Like a Scientist 1.4 Problem Solving in Chemistry
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• 1.4 Problem Solving in Chemistry > 2 Chapter 1 Vocabulary Physical chemistry Pure chemistry Applied chemistry Technology
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• 1.4 Problem Solving in Chemistry > 3 Physical chemistry the area of chemistry that deals with the mechanism, the rate, and the energy transfer that occurs when matter undergoes a change
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• 1.4 Problem Solving in Chemistry > 4 Pure chemistry the pursuit of chemical knowledge for its own sake
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• 1.4 Problem Solving in Chemistry > 5 Applied chemistry research that is directed toward a practical goal or application
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• 1.4 Problem Solving in Chemistry > 6 Technology the means by which a society provides its members with those things needed and desired
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• 1.4 Problem Solving in Chemistry > 7 Math Review Rounding Numbers A rounded number has about the same value as the number you start with, but it is less exact. Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 8 Rules for Rounding Here's the general rule for rounding: If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40 If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 33 rounded to the nearest ten is 30 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 9 What Are You Rounding to? When rounding a number, you first need to ask: what are you rounding it to? Numbers can be rounded to the nearest ten, the nearest hundred, the nearest thousand, and so on. Consider the number 4,827 4,827 rounded to the nearest ten is 4,830 4,827 rounded to the nearest hundred is 4,800 4,827 rounded to the nearest thousand is 5,000 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 10 Whole Numbers Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, (and so on) Fractions Part of a whole, number in between two whole numbers, can also be represented as decimals Example: 5/6 or 43.568 or 2.1 or 0.09 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 11 Rounding and Fractions Rounding fractions works exactly the same way as rounding whole numbers. The only difference is that you may now round to tenths, hundredths, thousandths, and so on. 7.8199 rounded to the nearest tenth is 7.8 1.0621 rounded to the nearest hundredth is 1.06 3.8792 rounded to the nearest thousandth is 3.879 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 12 Here's a tip: to avoid getting confused in rounding long decimals. Look only at the number in the place you are rounding to and the number that follows it. For example, to round 5.3824791401 to the nearest hundredth, just look at the number in the hundredths place8and the number that follows it2. Then you can easily round it to 5.38. Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 13 3,849.379285461 Round the above number to the following: nearest thousand 4,000 nearest hundred 3,800 nearest ten 3,850 nearest whole number 3,849 nearest tenth 3,849.4 nearest hundredth 3,849.38 nearest thousandth 3,849.379 nearest millionth 3,849.379285 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 15 597.352 Round to the nearest tenth A) 600 B) 597.3 C) 597.4 D) 597 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 16 45.445237 Round to the nearest ten A) 45.5 B) 45.45 C) 50 D) 45 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 17 252.6786 Round to the nearest hundred A) 300 B) 252.68 C) 252.67 D) 252.679 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 18 0.4444444 Round to the nearest thousandth A) 0.4444 B) 0.4 C) 0.444 D) 0.44444 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 19 5,369.4652 Round to the nearest thousand A) 5,000.5 B) 5,000 C) 5,369.465 D) 5,400 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 20 78,363.5528954394 Round to the nearest millionth A) 78,363.55290 B) 78,363.5528954 C) 78,363.5529 D) 78,363.552895 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 21 35.58 Round to the nearest whole number A) 40 B) 35.6 C) 36 D) 35 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 22 \$16.32 Round to the nearest dollar A) \$16.00 B) \$17.00 C) \$20.00 D) \$10.00 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 23 \$826.25 Round to the nearest tenth A) \$830.00 B) \$820.00 C) \$826.00 D) \$826.30 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.
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• 1.4 Problem Solving in Chemistry > 24 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Solving Numeric Problems The steps for solving a numeric word problem are analyze, calculate, and evaluate. AnalyzeEvaluate 213 Calculate
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• 1.4 Problem Solving in Chemistry > 25 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Solving Numeric Problems First determine where you are starting from (identify what is known) and where you are going (identify what is unknown). Analyze 1
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• 1.4 Problem Solving in Chemistry > 26 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Solving Numeric Problems First determine where you are starting from (identify what is known) and where you are going (identify what is unknown). If you expect the answer (the unknown) to be a number, you need to determine what unit(s) the answer should have. Make a plan for using what is known to arrive at the unknown. Analyze 1
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• 1.4 Problem Solving in Chemistry > 27 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Solving Numeric Problems For some problems, you will have to convert a measurement from one unit to another. For other problems, you may need to rearrange an equation before you can solve for an unknown. Calculate 2
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• 1.4 Problem Solving in Chemistry > 28 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Solving Numeric Problems After you calculate an answer, you should evaluate it. Evaluate 3
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• 1.4 Problem Solving in Chemistry > 29 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Solving Numeric Problems After you calculate an answer, you should evaluate it. Evaluate 3 Is the answer reasonable? Does it make sense? Did you copy the data correctly? Did you choose the right equations? Check that your answer has the correct unit(s) and the correct number of significant figures.
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• 1.4 Problem Solving in Chemistry > 30 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 1.1 Estimate Walking Time You are visiting Indianapolis. You decide to walk from the Indiana State Capital to the Murat Centre for an afternoon performance. According to the map, the shortest route from the capital to the theater is 8 blocks. How many minutes will the trip take if you can walk 1 mile in 20 minutes? Assume that 10 blocks equals 1 mile. Start Finish
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• 1.4 Problem Solving in Chemistry > 31 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Sample Problem 1.1 This problem is an example of a conversion problem. One unit of measure (blocks) must be expressed in a different unit (minutes). KNOWNS distance to be traveled = 8 blocks walking speed = 1 mile/20 minutes 1 mile = 10 blocks UNKNOWN time of trip = ? minutes Analyze List the knowns and the unknown. 1
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• 1.4 Problem Solving in Chemistry > 32 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Divide the number of blocks to be traveled by the number of blocks in 1 mile. Calculate Solve for the unknown. 2 Sample Problem 1.1 1 mile 10 blocks 8 blocks = 0.8 mile The relationship 1 mile = 10 blocks can be interpreted as 1 mile per 10 blocks.
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• 1.4 Problem Solving in Chemistry > 33 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Multiply the number of miles by the time it takes to walk 1 mile. Calculate Solve for the unknown. 2 Sample Problem 1.1 Notice how the units cancel. 20 minutes 1 mile 0.8 mile = 16 minutes
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• 1.4 Problem Solving in Chemistry > 34 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. The answer seems reasonable, 16 minutes to walk 8 blocks. The answer has the correct unit. The relationships used are correct. Evaluate Does the result make sense? 3 Sample Problem 1.1
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• 1.4 Problem Solving in Chemistry > 35 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Matthew wants to tip 15% on his bill of \$11.58. He can estimate 10% by moving the decimal over to the left one place and round to the nearest tenth. Then figure half that amout and add it to the earlier estimation. \$1.20 + \$0.60 = \$1.80 is about 15% of \$11.58 How would you estimate 20% of \$11.58? \$1.20 x 2 = \$2.40 is about 20% of \$11.58
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• 1.4 Problem Solving in Chemistry > 36 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved. Key Concepts The steps for solving a nonnumeric problem are analyze and solve. Effective problem solving always involves developing a plan and then implementing that plan. The steps for solving a numeric word problem are analyze, calculate, and evaluate.
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