Decimal Operations

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Chapter 2

• Decimal Operations

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2.1 Comparing, Ordering, Rounding Decimals

• Decimal-a that is written using the base-ten
  place value system where a decimal point
  separates the ones tenths digits. Each place
  value is 10 times the place value to its right.

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In the Real World

• Olympic Games In the 1968 Summer Olympics, Irena
  Szewinska of Poland won the womens 200 meter
  dash with a time of 22.5 seconds. In 1996,
  Marie-Jose Perec of France won with a time of
  22.12 seconds. Whose time is faster?

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Comparing Decimals

• When comparing decimals, write the numbers in a
  column, lining up the decimal points. Use zeros
  as placeholders if needed.
• 22.12
• 22.50

The tens ones digits are the same.
Add a zero as a placeholder.
The tenths digits are different. 5 gt 1
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Ordering Decimals

• Use the same method as comparing decimals. You
  can also use a number line to help you order.
• Order 2.11, 2.21, 2, 2.06, and 2.24 from least to
  greatest.

2.21
2.24
2
2.06
2.11
2.0
2.1
2.2
2.3
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Rounding Decimals

• To round a decimal to a given place value, look
  at the digit in the place to the right.
• 4 or less, give it a rest
• 5 or more, raise the score
• Ex. Round 7.126 to the nearest tenth.
• 7.126
• 7.1

The hundredths digit is less than 5, round down
and drop the remaining digits
You want to round to the nearest tenth.
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Your turn!

• 20.05_?_ 20.1
• 5.701_?_ 5.699
• Order 8.11, 8, 8.03, 8.85, 8.42 least to
  greatest.
• Order 3.84, 4.4, 4.83, 3.48, 4.38 (L to G)
• Round 10.458 to the nearest tenth.
• Round 34.0152 to the nearest hundredth.

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Answers

• lt less
• gt greater
• 8, 8.03, 8.11, 8.42, 8.75
• 3.48, 3.84, 4.38, 4.4, 4.83
• 10.5
• 34.02

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2.2 Adding Subtracting Decimals

• Front-end estimation-to estimate a sum, add the
  front-end digits, estimate the sum of the
  remaining digits, and then add the result.

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Adding Subtracting Decimals

• When adding/subtracting decimals use a vertical
  format. Line up the decimals first and use zeros
  as placeholders when needed.
• 6.047 13.46
• 6.047
• 13.460
• 19.507

Write zero as a placeholder
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Evaluating a Variable Expression

• Substitute the variables with the given values.
  Dont forget to add/subtract from left to right
  when evaluating horizontally.
• Evaluate 6.7 r t when r 2.14 and t 5.2.
• 6.7 2.14 5.2
• 8.84 5.2
• 3.64

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Estimating a Sum

• Video Games For your birthday you receive a 25
  gift certificate. You want to buy 3 used video
  games whose prices are 8.79, 7.29, 7.89. Can
  you buy all 3 games using the gift certificate?

8.79 7.29 7.89
8.79 7.29 7.89 22
1 1 2
1) Add the front-end digits the dollars.
2) Estimate the sum of the remaining digits the
cents.
22 1 24
3) Add the results.
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Your turn!

• 13.8 9.3
• 1.6 0.8
• Evaluate the expression when a 4.2 and
• b 6.27
• 3. a b
• 4. 10.03 a b
• Evaluate using front-end estimation
• 5. 5.24 9.79
• 6. 6.6 4.45

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Answers

• 23.1
• 0.8
• 10.47
• 12.1
• 15
• 2

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2.3 Multiplying Decimals

• Leading digit-the first nonzero digit
• Multiply decimals as you would whole numbers.
  Then place the decimal point in the product. The
  of decimal places in the product is equal to
  the sum of the number of decimal places in the
  factors.
• 0.7 x 0.3 0.21

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Multiplying decimals
5.82 X 0.41 582 23280 2.3862

• Checking Reasonableness to check that the product
  is reasonable, round each factor to the place
  value of the leading digit, then multiply.

5.82 6 Round to nearest whole 0.41 0.4 Round
to nearest tenth Because 6 x 0.4 2.4, the
product is reasonable
2 decimals places 2 decimal places 4 decimal
places
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Multiplying Decimals to find Area

• Central Park Central Park is a rectangular park
  about 2.5 miles long and about 0.5 mile wide.
  What is the area of Central Park?
• A l x w
• 2.5(0.5)
• 1.25
• The area of Central Park is about 1.25 square
  miles.

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Your turn!

• What is the leading digit in the decimal 0.00462?
• 0.4 x 0.6 3. 0.9 x 0.91
• 4. Laura has 10 to spend on nail polish.
  Including tax, each bottle costs 2.89. Can Laura
  buy 3 bottles of polish? Explain.
• 5.Estimate 0.32 x 2.8
• 6.

6.04 yd
8.76 yd
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Answers

• 4
• 0.24
• 0.819
• Yes, each bottle is less than 3 and
• 3 x 3 9
• 5. 0.9
• 6. 52.9104 yd2

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2.4 Dividing Decimals

• Compatible numbers-numbers that make a
  calculation easier.
• You can use long division to divide a decimal by
  a whole . Divide as with whole numbers. Then
  lineup the decimal points in the quotient the
  dividend.

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In the Real World

• Ticket prices The cost of 21 tickets to see the
  Blue Man Group is 761.25. How much does each
  ticket cost?
• To find the cost divide 761.25 by 21.
• _36.25_
• 21)761.25
• Checking Reasonableness use compatible to check
  for reasonableness.

• 20 Round divisor to place of
  leading digit
• 761.25 760 Round dividend to nearest
  multiple of 20
• Because 760 20 38, the quotient is
  reasonable.

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Dividing by a Decimal

• When you divide by a decimal, multiply both the
  divisor the dividend by a power of 10 that will
  make the divisor a whole .
• Dont forget to use zeros as placeholders in the
  quotient.
• 8.75 12.5
• 0.7

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Rounding a Quotient

• Trading Cards You buy a pack of 8 trading cards
  for 1.49. find the price of each card. Round to
  the nearest cent.
• Divide 1.49 by 8
• 1.49 8 0.186
• Round the quotient to the nearest cent.
• .186 .19

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Your Turn!

• What two compatible would you use to estimate
  the quotient 54.2 6.7?
• 3.45 15
• 12.74 2.6
• 80.84 9.4
• You are knitting a scarf using 4 balls of yarn.
  The yarn costs a total of 24.88. How much does 1
  ball of yarn cost?

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Answers

• 56 and 7
• 0.23
• 4.9
• 8.6
• 6.22

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2.5 Scientific Notation

• Scientific notation a is written in
  scientific notation if it has the form c x 10n
  where c is greater than or equal to 1 and less
  than 10, and n is an integer.
• Standard form Product form Scientific form
• 2,860,000 2.86 x 1,000,000 2.86 x 106

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In the Real World

• Mars has two moons, Phobos Deimos. Phobos has
  a mass of 1.06 x 1016 kg. Deimos has a mass of
  2.4 x 1015 kg. Which moon has a greater mass?
• First compare the exponents. If exponents are
  equal, then compare the decimal parts.
• Because 16 gt 15,
• then 1.06 x 1016 gt 2.4 x 1015
• Phobos has a greater mass.

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2.6 Measuring in Metric Units
Metric system-decimal system of measurement that
has units for length, mass, and capacity.

• Length
• Meter- basic unit of length
• Millimeter
• Centimeter
• Kilometer

Capacity-measure of the amount that a container
can hold. Liter Milliliter Centiliter Kiloliter

• Mass-the amount of matter that an object has.
• Gram
• Milligram
• Kilogram

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2.7 Converting Metric Units
To convert between metric units n decimal places
apart, multiply or divide as follows. Multiply
by 10n Larger unit Smaller unit Divide by 10n
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In the Real World

• Running
• In the 4 x 800 meter relay race, four teammates
  each run 800 meters. The total length of the race
  is 3200 meters. How man kilometers long is the
  race?
• 3200 1000 3.2