Chapter 3 - Decimals

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Chapter 3 - Decimals

• Math Skills Week 4

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Outline

• Introduction to Decimals Section 3.1
• Addition of Decimals Section 3.2
• Subtraction of Decimals Section 3.3
• Multiplication of Decimals Section 3.4
• Division of Decimals Section 3.5
• Comparing and Converting Fractions and Decimals
  Section 3.6

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Stuff to Remember (forget???)

• Reduce all fractional answers to simplest form,
  and convert improper fractions to mixed numbers
• MIDTERM Next Class
• Chapters 1, 2, and 3
• Study tips
• review slides
• your notes
• read sections in the book
• look at example problems in book
• Pay attention to what question is asking
• Prime factorization vs. Finding all factors
• On homework/quizzes, clearly circle your answer
• Class Project Handout

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Introduction to Decimals

• This is a number in decimal notation
• The decimal part represents a number less than
  one
• Just like 61.88, 88 represents 88 cents, which
  is less than 1.

61.88
Decimal part
Whole Number part
Decimal Point
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Introduction to Decimals

• Just as with whole numbers, decimal numbers have
  place values
• The position of a digit in a decimal determines
  the digits place value
• 0 is in the hundredths, 3 is in the tenths
• 9 is in the _______ place
• 4 is in the _______ place

hundreds
tens
ones
Ten-thousandths
hundred-thousandths
tenths
hundredths
thousandths
millionths
.
4
5
8
3
0
2
7
1
9
millionths
hundredths
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Introduction to Decimals

• Rounding decimals is similar to rounding whole
  numbers.
• Approximate the decimal to any place value
• Steps
• Write out the number to be rounded in a place
  value chart
• Look at the number to the right of the place
  value you are rounding to.
• If the number is gt or 5, increase the digit in
  the place value by 1, and remove all digits to
  the right of it
• If the number is lt 5, remove it and all of the
  digits to the right of it.
• Examples
• Round 0.46972 to the nearest thousandth
• 0.470
• Round 0.635457 to nearest hundred thousandths
• 0.63546

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Introduction to Decimals

• Class Examples
• Round 48.907 to the nearest tenth
• 48.9
• Round 31.8562 to the nearest whole number
• 32
• Round 3.675849 to the nearest ten-thousandth
• 3.6758

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Addition/Subtraction of Decimals

• Adding and subtracting decimal numbers is the
  similar as adding and subtracting whole numbers
• Catch first align the decimal points of each
  number on a vertical line.
• Assures us that we are adding/subtracting digits
  that are in the same place value

4290.3
000
16290.903
0
65.0729
20646.2759
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Addition/Subtraction of Decimals

• Examples (Addition)
• Add0.83 7.942 15
• 23.772
• Add 23.037 16.7892
• 39.8262
• Class Examples (Addition)
• Find the sum of 4.62, 27.9, and 0.62054
• 33.14054
• Add 6.05 12 0.374
• 18.424

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Addition/Subtraction of Decimals

• Examples (Subtraction)
• Subtract 39.047 7.96
• 31.087
• Find 9.23 less than 29
• 19.77
• Class Examples (Subtraction)
• Subtract 72.039 8.47
• 63.569
• Subtract 35 9.67
• 25.33

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Multiplication of Decimals

• Multiplication of decimals is similar to
  multiplication of whole numbers.
• Question Where does decimal go?
• Check this
• 0.3 x 5 1.5
• Start with 1 decimal place, answer has 1 decimal
  place
• 0.3 x 0.5 0.15
• Start with a total of 2 decimal places, answer
  has 2 decimal places
• 0.3 x 0.05 0.015
• Start with a total of 3 decimal places, answer
  has 3 decimal places

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Multiplication of Decimals

• Multiplication Steps
• Do the multiplication as if it were whole numbers
• To place the decimal in the right location
• Count the total number of decimal places in all
  of the factors
• Starting from the right of the product, count the
  total number of decimal places towards the left,
  and place the decimal point there.

21.4 x 0.36
3 total decimal places
7 704
.
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Multiplication of Decimals

• Examples
• 920 x 3.7
• 3404.0
• 0.00079 x 0.025
• 0.00001975
• Class Examples
• 870 x 4.6
• 4002.0
• 0.000086 x 0.057
• 0.000004902

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Multiplication of Decimals

• To multiply a decimal by a power of 10 (for
  example 10, 100, 1,000 etc.) move the decimal to
  the right the same number of times as there are
  zeros.
• 3.8925 x 10
• 38.925
• 3.8925 x 100
• 389.25
• 3.8925 x 1000
• 3892.5
• 3.8925 x 10000
• 38925.0
• 3.8925 x 100000
• 389250.0 (Note we added a zero before the
  decimal)

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Division of Decimals

• Dividing decimals is similar to dividing whole
  numbers.
• Same questionwhat about the decimal place? Where
  does that go?
• Steps
• Make the divisor a whole number by shifting the
  decimal to the right as many times as necessary.
• Move the decimal in the dividend the same number
  of times that we moved it in the divisor

7 0 6
4 2 0 9
.
.
0
??????
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Division of Decimals

• Dividing decimalscontd
• Steps
• Add zeros to the end of the dividend so that we
  can round to the desired place value
• Example Round quotient to nearest tenth ? write
  2 zeros after the decimal
• Round quotient to nearest thousandth ? need 4
  zeros after the decimal

706
42090.00
706
42090.0000
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Division of Decimals

• Dividing decimalscontd
• Steps
• Do the division as if it were whole numbers
• Put the decimal place in the quotient directly
  over the decimal point in the dividend

00059.61 59.6
706
42090.00
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Division of Decimals

• Examples
• Divide 58.092 82 round to the nearest
  thousandth
• 0.7084 0.708
• Divide 420.9 7.06, round to the nearest tenth
• 59.61 59.6
• Divide 2.178 0.039, round to the nearest
  hundredth
• 55.85

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Division of Decimals

• Class Examples
• Divide 37.042 76 round to the nearest
  thousandth
• 0.4873 0.487
• Divide 370.2 5.09, round to the nearest tenth
• 72.73 72.7

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Division of Decimals

• To divide a decimal by a power of 10 (for example
  10, 100, 1,000 etc.) move the decimal to the left
  the same number of times as there are zeros. Fill
  in the blank spaces with zeros.
• 34.65 10 or 101
• 3.465
• 34.65 100 or 102
• 0.3465
• 34.65 1000 or 103
• 0.03465
• 34.65 10000 or 104
• 0.003465

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Comparing Converting Fractions Decimals

• Fractions and decimals are two ways of
  representing parts of a whole number.
• ¼ is a portion of 1 whole
• 0.345 is a portion of 1 whole
• Every fraction can be written as a decimal
• Every decimal can be written as a fraction

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Comparing Converting Fractions Decimals

• To convert a fraction ? decimal
• Steps
• Divide the numerator of the fraction by the
  denominator
• Round the quotient to a desired place value
• Example
• Convert 3/7 to a decimal and round to nearest
  Hundredth and Thousandth
• 0.42857
• Nearest Hundredth 0.43
• Nearest Thousandth 0.429

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Comparing Converting Fractions Decimals

• Examples
• Convert 3/8 to a decimal round to nearest
  hundredth
• 0.375 0.38
• Convert 2 ¾ to a decimal round to nearest tenth
• 2.75 2.8
• Class Examples
• Convert 9/16 to a decimal round to nearest tenth
• 0.6
• Convert 4 1/6 to a decimal round to nearest
  hundredth
• 4.17

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Comparing Converting Fractions Decimals

• To convert a decimal ? fraction
• Steps
• Count the number of decimal places
• Remove the decimal point (and any leading zeros)
• Put the decimal part over a denominator,
• The denominator is a factor of 10 that has the
  same number of zeros as decimal places (from step
  1)
• Put the fraction in simplest form
• Example
• Convert 0.47 to a fraction
• 47/100
• Convert 0.275 to a fraction
• 275/1000 11/40

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Comparing Converting Fractions Decimals

• Examples
• Convert 0.82 to a fraction
• 82/100 2?41 / 2?50 41/50
• Convert 4.75 to a fraction
• 4 75/100 4 3?25/4?25 4 3/4
• Class Examples
• Convert 0.56 to a fraction
• 56/100 4?14 / 4?25
• Convert 5.35 to a fraction
• 5 35/100 5 7?5 / 5?20 5 7/20

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Comparing Converting Fractions Decimals

• The order relation between two decimals tells us
  which decimal is larger than the other
• Example Which is larger 0.88 or 0.088?
• 0.88
• Think of this like money
• 0.88 is like 0.88 88 cents
• 0.088 is 0.09 9 cents
• Comparing decimals is easy, what about comparing
  a decimal to a fraction?
• Which is larger 5/6 or 0.625?
• Question What to do?
• Convert 5/6 ? Decimal OR
• Convert 0.625 ? fraction

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Comparing Converting Fractions Decimals

• Examples
• Find the order relation between 3/8 and 0.38
• 3/8 0.375 lt 0.380 ? 3/8 lt 0.38
• Class Example
• Find the order relation between 5/16 and 0.32
• 5/16 0.313 lt 0.32 ? 5/16 lt 0.32