Mathematics: Applications and Concepts, Course 1 Interactive Chalkboard
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Lesson 3-1 Representing Decimals
Lesson 3-2 Comparing and Ordering Decimals
Lesson 3-3 Rounding Decimals
Lesson 3-4 Estimating Sums and Differences
Lesson 3-5 Adding and Subtracting Decimals
Example 1 Write a Decimal in Word Form
Example 2 Standard Form and Expanded Form
Write 102.056 in word form.
Answer: 102.056 is one hundred two and fifty-six
thousandths.
Write 230.108 in word form.
Answer: two hundred thirty and one hundred eight
thousandths
Write seventy-six and one hundred three
thousandths in standard form and in expanded form.
Answer:
Standard form: 76.103
Expanded form:
Write fifty-nine and sixty-two thousandths in standard
form and in expanded form.
Answer:
Standard form: 59.062
Expanded form: (5  10) (9  1) (0  0.1)
(6  0.01) (2  0.001)
Example 1 Compare Decimals
Example 2 Order Decimals
BASEBALL The table below lists the final winning
percents for several American League baseball teams
in 2001. Use > or < to compare New York’s percent
with Cleveland’s percent.
2001 Final Standings
Team
Percent Standings
New York
0.594
Boston
0.509
Cleveland
0.562
Detroit
0.407
Source: www.espn.com
Method 1 Use place value.
First, line up the
decimal points.
New York:
Cleveland:
Then, starting at the
left, find the first place
the digits differ.
Compare the digits.
Since 9 > 6, 0.594 > 0.562.
Method 2 Use a number line.
Numbers to the right are greater than numbers to the left.
Since 0.594 is to the right of 0.562, 0.594 > 0.562.
Answer: 0.594 > 0.562; New York had the higher winning
percentage.
EXAMS In Mr. Smith’s math class, 29.65% of the
students earned a grade of “A” at the end of the
semester. In Mrs. Dempsey’s class, 29.85% of the
students earned a grade of “A” at the end of the
semester. Use > or < to compare the percent in Mr.
Smith’s class with the percent in Mrs. Dempsey’s class.
Answer: 29.65% < 29.85%
Order 25, 25.1, 24.36, and 25.03 from least to greatest.
First, line up
the decimal
points.
25

25.00
25.1

25.10
24.36 
24.36
25.03 
25.03
Next, annex zeros
so that each has the
same number of
decimal places.
Finally, use place
value to compare
the decimals.
Answer: The order from least to greatest is 24.36, 25,
25.03, and 25.1.
Order 71, 71.04, 70.89, and 71.4 from least to greatest.
Answer: 70.89, 71, 71.04, 71.4
Example 1 Round Decimals
Example 2 Round Decimals
Example 3 Use Rounding to Solve a Problem
Round 7.601 to the nearest whole number.
Underline the digit
to be rounded. In
this case, the
ones place.
7.601
Then look at the digit to
the right. Since 6 is
greater than 5, add one
to the underlined digit.
On the number line, 7.6 is closer to 8.0 than 7.0.
Answer: To the nearest whole number, 7.601 rounds to 8.0.
Round 4.321 to the nearest whole number.
Answer: 4
Round 68.94 to the nearest tenth.
Underline the digit
to be rounded. In
this case, the
digit is in the
tenths place.
68.94
Then look at the digit to
the right. Since the digit
is 4, the digit 9 stays
the same.
On the number line, 68.94 is closer to 68.9 than 69.0.
Answer: To the nearest tenth, 68.94 rounds to 68.9
Round 125.38 to the nearest tenth.
Answer: 125.4
EARNINGS In the year 2000, the average hourly wage
for a U.S. production worker was $13.75. How much is
this to the nearest dollar? The average weekly
earnings were $474.38. What is this to the nearest
dollar?
To round to the nearest dollar, round to the nearest ones.
Underline the digit
in the ones place.
$13.75
Then look at the digit to
the right. The digit is
greater than 5. So, add
one to the underlined digit.
Answer: To the nearest dollar, the average hourly wage
was $14.00.
Round $474.38 to the nearest ones.
$474.38  $474.00
Since 3 is less than 5, the digit in
the ones place remains the same.
Answer: To the nearest dollar, the average weekly
earnings were $474.00.
CEREAL The price per ounce for a box of cereal is
shown as $0.1275 on the tag in the grocery store.
How much is this to the nearest cent?
Answer: $0.13
Example 1 Use Estimation to Solve Problems
Example 2 Use Estimation to Solve Problems
Example 3 Use Front-End Estimation
Example 4 Use Clustering
POPULATION The table below shows the population
of the American colonies in 1770. Estimate the total
population of North Carolina and South Carolina.
Colony
Connecticut
Population
(thousands)
183.9
Colony
Population
(thousands)
New York
162.9
Delaware
35.5
North Carolina
197.2
Georgia
23.4
Pennsylvania
240.1
Maryland
202.6
Rhode Island
58.2
Massachusetts
235.3
South Carolina
124.2
New Hampshire
62.4
Virginia
447.0
New Jersey
117.4
Round each number to the nearest hundred for easier
adding.
197.2 

200
100
197.2 rounds to 200.
124.2 rounds to 100.
300
Answer: There were about 300 thousand people in
North Carolina and South Carolina.
POPULATION The table below shows the population of
the American colonies in 1770. Estimate how many
more people were in Massachusetts than in
Connecticut.
Colony
Connecticut
Delaware
Georgia
Maryland
Massachusetts
New Hampshire
New Jersey
Population
(thousands)
183.9
35.5
23.4
202.6
235.3
62.4
117.4
Colony
New York
North Carolina
Pennsylvania
Rhode Island
South Carolina
Virginia
Answer: about 60 thousand more people
Population
(thousands)
162.9
197.2
240.1
58.2
124.2
447.0
POPULATION The table below shows the population of
the American colonies in 1770. Estimate how many
more people lived in Rhode Island than in Georgia in
1770.
Colony
Connecticut
Delaware
Georgia
Maryland
Massachusetts
New Hampshire
New Jersey
Population
(thousands)
183.9
35.5
23.4
202.6
235.3
62.4
117.4
Colony
New York
North Carolina
Pennsylvania
Rhode Island
South Carolina
Virginia
Population
(thousands)
162.9
197.2
240.1
58.2
124.2
447.0
Round each number to the nearest ten for easier
subtracting.
58.2

60
58.2 rounds to 60.
– 23.4

– 20
23.4 rounds to 20.
40
Answer: There were about 40 thousand more people.
POPULATION The table below shows the population
of the American colonies in 1770. Estimate the total
number of people in Pennsylvania and New Jersey in
1770.
Colony
Connecticut
Delaware
Georgia
Maryland
Massachusetts
New Hampshire
New Jersey
Population
(thousands)
183.9
35.5
23.4
202.6
235.3
62.4
117.4
Colony
New York
North Carolina
Pennsylvania
Rhode Island
South Carolina
Virginia
Answer: about 300 thousand people
Population
(thousands)
162.9
197.2
240.1
58.2
124.2
447.0
Estimate
Add the front digits.
14.8
+ 55.9
6
using front-end estimation.

Then add the next digits.
14.8
+ 55.9
Answer: Using front-end estimation,
69
is about 69.
Estimate
Answer: 97
using front-end estimation.
MULTIPLE-CHOICE TEST ITEM A cage of guinea pigs
at the pet store is given a vitamin-water solution each
day. Last week the guinea pigs consumed 21.8
ounces, 19.1 ounces, 20.3 ounces, 18.9 ounces, and
22.0 ounces of the solution each day. Use this
information to estimate the total amount of vitamin
solution consumed in one day.
A 70 oz
B 90 oz
C 100 oz
D 120 oz
Read the Test Item
The addends are all clustered around 20.
17.8
→
20
19.1
→
20
20.3
→
20
18.9
→
20
+ 22.0
→
+ 20
100
Solve the Test Item
Multiplication is repeated addition. So, a good estimate
is 5  20, or 100.
Answer: C
MULTIPLE-CHOICE TEST ITEM During the month of
February, Jonathon spends $14.78 on gasoline the
first week, $15.35 on gasoline during the second week,
$15.94 on gasoline during the third week, and $14.07
on gasoline during the fourth week. Use this
information to estimate the total amount Jonathon
spent on gasoline during February.
A $35
Answer: C
B $50
C $60
D $100
Example 1 Add Decimals
Example 2 Subtract Decimals
Example 3 Annex Zeros
Example 4 Use Decimals to Solve a Problem
Example 5 Evaluate an Expression
Find the sum of 75.6 and 21.3.
Estimate
75.6
+ 21.3
96.9
Line up the decimal points.
Compare the answer to
the estimate. Since
Add as with whole numbers. 96.9 is close to 97, the
answer is reasonable.
Answer: The sum of 75.6 and 21.3 is 96.9.
Find the sum of 34.6 and 53.2.
Answer: 87.8
Find 10.756 – 6.238.
Estimate
10.756
– 6.238
4.518
Line up the decimal points.
Subtract as with whole numbers.
Answer:
Compare to the
estimate.
Find 24.758 – 18.315.
Answer: 6.443
Find 8 – 1.74.
Estimate
8.00
– 1.74
6.26
Answer:
Annex zeros.
Compare to the estimate.
Find 9 – 3.28.
Answer: 5.72
PIZZA Joe’s Pizza Shop sells an average of 89.7 pizzas
on Tuesday nights and an average of 210.5 pizzas on
Saturday nights. How many more pizzas does Joe’s
Pizza Shop sell on Saturdays?
Estimate
210.5
– 89.7
120.8
Answer: Joe’s Pizza Shop sells an average of 120.8
more pizzas on Saturdays.
MOVIES The local movie theater sells an average of
65.8 tickets on Thursdays and an average of 288.9
tickets on Saturdays. How many more tickets are sold
on Saturdays?
Answer: 223.1 tickets
ALGEBRA
Replace a with 10.75 and b with 4.8.
Estimate
10.75
– 4.80
5.95
Line up the decimal points.
Annex a zero.
Subtract as with whole numbers.
Answer: The value is 5.95. This value is close to the
estimate. So, the answer is reasonable.
ALGEBRA
Answer: 70.13
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