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1.4 Problem Solving in Chemistry >1.4 Problem Solving in Chemistry >

1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Chapter 1Introduction to Chemistry

1.1 The Scope of Chemistry1.2 Chemistry and You1.3 Thinking Like a Scientist

1.4 Problem Solving in Chemistry


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Chapter 1 Vocabulary•Physical chemistry

•Pure chemistry

•Applied chemistry•Technology


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Physical chemistrythe 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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Pure chemistrythe pursuit of chemical knowledge for its own sake


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Applied chemistryresearch that is directed toward a practical goal or application


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Technologythe means by which a society provides its members with those things needed and desired


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Math Review

Rounding Numbers

A rounded number has about the same value as the number you start with, but it is less exact.

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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



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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



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Whole NumbersWhole Numbers are simply the numbers 0, 1, 2,

3, 4, 5, … (and so on)

FractionsPart 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



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Rounding and FractionsRounding 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



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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 place—8—and the number that follows it—2. Then you can easily round it to 5.38.



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3,849.379285461Round 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



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Let’s Practice



15

597.352

Round to the nearest tenth

A) 600

B) 597.3

C) 597.4

D) 597



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45.445237

Round to the nearest ten

A) 45.5

B) 45.45

C) 50

D) 45



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252.6786Round to the nearest hundred

A) 300

B) 252.68

C) 252.67

D) 252.679



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0.4444444

Round to the nearest thousandth

A) 0.4444

B) 0.4

C) 0.444

D) 0.44444



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5,369.4652

Round to the nearest thousand

A) 5,000.5

B) 5,000

C) 5,369.465

D) 5,400



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78,363.5528954394

Round to the nearest millionth

A) 78,363.55290

B) 78,363.5528954

C) 78,363.5529

D) 78,363.552895



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35.58Round to the nearest whole number

A) 40

B) 35.6

C) 36

D) 35



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$16.32

Round to the nearest dollar

A) $16.00

B) $17.00

C) $20.00

D) $10.00



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$826.25

Round to the nearest tenth

A) $830.00

B) $820.00

C) $826.00

D) $826.30




Solving Numeric Solving Numeric ProblemsProblems

The steps for solving a numeric word problem are analyze, calculate, and evaluate.

Analyze Evaluate

21 3

Calculate




• First determine where you are starting from (identify what is known) and where you are going (identify what is unknown).

Analyze 1




• 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




• 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




After you calculate an answer, you should evaluate it.

Evaluate 3




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.



Sample Problem 1.1Sample 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




This problem is an example of a conversion problem. One unit of measure (blocks) must be expressed in a different unit (minutes).

KNOWNSdistance to be traveled = 8 blockswalking speed = 1 mile/20 minutes1 mile = 10 blocks

UNKNOWN

time of trip = ? minutes

Analyze List the knowns and the unknown.1



Divide the number of blocks to be traveled by the number of blocks in 1 mile.

Calculate Solve for the unknown.2


1 mile10 blocks8 blocks = 0.8 mile

The relationship 1 mile = 10 blocks can be interpreted as “1 mile per 10 blocks.”



Multiply the number of miles by the time it takes to walk 1 mile.

Calculate Solve for the unknown.2


Notice how the units cancel.

20 minutes1 mile0.8 mile = 16 minutes



• 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




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



Key ConceptsKey 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.



END OF 1.4END OF 1.4

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