Chapter 6 Decimal Review (plus more)

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Chapter 6Decimal Review (plus more)
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Slideshow Outline

• Introduction to Decimals
• Order and Rounding
• Adding and Subtracting Decimals
• Multiplying Decimals and Circumference of a
  Circle
• Dividing Decimals and Order of Operations
• Fractions and Decimals

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• Introduction to (review of) Decimals

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Section Objectives

• Decimal Notation and Writing Decimals in Words
• Writing Decimals in Standard Form
• Writing Decimals as Fractions
• Writing Fractions as Decimals

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Decimal Notation and Writing Decimals in Words
Definition Example
Decimal Numbers Numbers written in decimal notation.
Decimal part
Whole number part
Decimal point
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Decimal Notation and Writing Decimals in Words
EXAMPLE
Write 47.65 in words.
SOLUTION
4 7 . 6 5
Forty-seven
and
sixty-five
hundredths.
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Writing Decimals in Standard Form
EXAMPLE
Write twelve and six hundredths in standard form..
SOLUTION
twelve
and
six hundredths
1 2
0 6
.
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Writing Decimals as Fractions
Decimal In Words Fraction
0.5 five tenths
0.36 thirty-six hundredths
0.002 two thousandths
0.07 seven hundredths
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Writing Fractions as Decimals
EXAMPLE
Write as a decimal. (Hint When the
denominator is a power of 10, we can write it by
reversing the procedure used in Slide 7.)
SOLUTION
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• Order and Rounding

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Section Objectives

• Comparing Decimals
• Rounding Decimals

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Comparing Decimals
Comparing Two Decimals

To compare decimals, compare digits in the same
place values from left to right.
EXAMPLE
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Rounding Decimals
EXAMPLE
Round 0.5942 to the nearest thousandth.
SOLUTION
Step 1 Locate the digit to the right of the
given place value.
0.5942
2 is to the right of the thousandth place value.
Step 2 If this digit is 5 or greater, add 1 to
the digit in the given place value and delete all
digits to its right. If this digit is less than
5, delete all digits to the right of the given
place value.
Since 2 is less than 5, we delete all digits to
the right of the thousandths place value.
0.5942
0.594
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Adding and Subtracting Decimals
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Section Objectives

• Adding Decimals
• Subtracting Decimals
• Estimating While Adding or Subtracting Decimals
• Solving problems by Adding or Subtracting Decimals

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Adding Decimals
Step Example
Step 1 Write the decimals so that the decimal points line up vertically. Add 0.004 0.085
Step 2 Add or subtract as with whole numbers.
Step 3 Place the decimal point in the sum or difference so that it lines up vertically with the decimal points in the problem.
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Subtracting Decimals
EXAMPLE
Subtract 3.3 from 28.
SOLUTION
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Estimating When Adding or Subtracting Decimals
EXAMPLE
Subtract 2.1 from 7.6.
SOLUTION
Exact
Estimate
Since 5.5 is close to 6, our answer is reasonable.
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Solving Problems by Adding or Subtracting Decimals
EXAMPLE
A pair of eyeglasses costs a total of 347.89.
The frames of the glasses are 97.23. How much
do the lenses of the eyeglasses cost?
SOLUTION
The lenses of the eyeglasses cost 250.66.
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Multiplying Decimals and Circumference of a
Circle
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Section Objectives

• Multiplying Decimals
• Estimating When Multiplying Decimals
• Multiplying by Powers of 10
• Finding the Circumference of a Circle
• Solving Problems by Multiplying Decimals

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Multiplying Decimals
Step Example
Step 1 Multiply the decimals as though they are whole numbers. Multiply
Step 2 The decimal point in the product is placed so that number of decimal places in the product is equal to the sum of the number of decimal places in the factors.
Total of 2 decimal places.
Decimal placed at two decimal places.
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Estimating When Multiplying Decimals
EXAMPLE
Multiply
SOLUTION
Exact
Estimate
Since 22.26 is close to our estimate of 20, it is
a reasonable answer.
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Multiplying by Powers of 10
Type Example
Multiplying Decimals by Powers of 10 such as 10, 100, 1000 . . . Move the decimal point to the right the same number of places as there are zeros in the power of 10.
Multiplying Decimals by Powers of 10 such as .1, .01, .001 . . . Move the decimal point to the left the same number of places as there are decimal places in the power of 10.
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Finding the Circumference of a Circle
Definition Example
Circumference The distance around a circle.
radius
diameter
or
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Finding the Circumference of a Circle
EXAMPLE
Find the circumference of the following circle.
9.1 yards
SOLUTION
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Solving Problems by Multiplying Decimals
EXAMPLE
Jose Severos, an electrician for Central Power
and Light, worked 40 hours last week. Calculate
his pay before taxes for last week if his hourly
wage is 13.88.
SOLUTION
Jose Severos pay before taxes for last week is
555.20.
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Dividing Decimals and Order of Operations
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Section Objectives

• Dividing Decimals
• Estimating When Dividing Decimals
• Dividing Decimals by Powers of 10
• Solving Problems by Dividing Decimals
• Simplifying Expressions with Decimals

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Dividing Decimals
Dividing by a Whole Number Example
Step 1 Place the decimal point in the quotient directly above the decimal point in the dividend.
Step 2 Divide as with whole numbers.
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Dividing Decimals
Dividing by a Decimal Example
Step 1 Move the decimal point in the divisor to the right until the divisor is a whole number.
Step 2 Move the decimal point in the dividend to the right the same number of places as the decimal point was moved in step 1.
Step 3 Divide. Place the decimal point in the quotient directly over the moved decimal point in the dividend
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Estimating When Dividing Decimals
EXAMPLE
Divide
SOLUTION
Exact
Estimate
Since 0.045 is close to our estimate of 0.05, the
answer is reasonable.
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Dividing Decimals by Powers of 10
Type Example
Dividing Decimals by Powers of 10 such as 10, 100, 1000 . . . Move the decimal point to the left the same number of places as there are zeros in the power of 10.
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Solving Problems by Dividing Decimals
EXAMPLE
Dorren Schmidt pays 73.86 per month to pay back
a loan of 1772.64. In how many months will the
loan be paid off?
SOLUTION
Dorrin Schmidt will have his loan paid off in 24
months.
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Simplifying Expressions with Decimals
Order of Operations
1. Perform all operations within parentheses ( ), brackets , or other grouping symbols such as fraction bars or square roots.
2. Evaluate any expressions with exponents.
3. Multiply or divide in order from left to right.
4. Add or subtract in order from left to right.
EXAMPLE
Simplify 1.4(2-1.8).
SOLUTION
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Fractions and Decimals
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Section Objectives

• Writing Fractions as Decimals
• Comparing Decimals and Fractions
• Solving Area Problems Containing Fractions and
  Decimals

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Writing Fractions as Decimals
EXAMPLE
Write as a decimal.
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 38
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Comparing Decimals and Fractions
Original numbers
Decimals
Compare
Thus,
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Solving Area Problems Containing Fractions and
Decimals
EXAMPLE
The area of a triangle is

Find the area of the following triangle.

4.4 feet
17 feet
SOLUTION
Write as .5.