Chapter 3: Lessons 3-1 to 3-4
STUDY GUIDE
This study guide provides you with an overview of the types of problems and skills that we will learn or have learned in the lessons listed above. In addition to this guide, we will complete additional review problems in class, as we get closer to the quiz.
Lesson 3-1: Representing Decimals
Example 1 Write a Decimal in Word Form
Write 24.408 in word form.
24.408 is twenty-four and four hundred eight thousandths.
Example 2 Standard Form
Write thiry-six and five thousandths in standard form.
Standard form:36.005
Lesson 3-2: Comparing and Ordering Decimals
Example 1 Compare Decimals
How to Compare Decimals
1) First, line up the decimal points.
2) Then, starting at the left, find the first place the digits differ.
3)Compare the two digits using >, < or =.
WEIGHT On the same scale, Jeremy weighs 93.7 pounds and Jeffrey weighs 93.2 pounds. Use > or < to compare Jeremy’s weight with Jeffrey’s weight.
Use place value.
Jeremy:93.7First, line up the decimal points.
Jeffrey:93.2Then starting at the left, find the first place the digits differ.
Compare the digits.
Since 7 > 2, 93.7 > 93.2.
Example 2 Order Decimals
How to Order Decimals
1) First, line up the decimal points.
2)Annex zeros so that each has the same number of decimal places.
3)Use place value to compare and order the decimals.
Order 34.03, 34, 33.98, and 34.1 from least to greatest.
34.03 → 34.0333.98
34 → 34.0034.00
33.98 → 33.9834.03
34.1 → 34.1034.10
The order from least to greatest is 33.98, 34, 34.03, and 34.1.
Lesson 3-3: Rounding Decimals
Example 1 Round Decimals
Round 4.629 to the nearest whole number.
4.629
Look at the number to the right of the number you underlined.
(Think – does the 6 tell you to keep it a 4 or change it to a 5?)
If it is five or more, add one more.
4.629 rounded to the nearest whole number is 5.
Example 2 Round Decimals
Round 35.62 to the nearest tenth.
35.62
Look at the number to the right of the number you underlined.
(Think – does the 2 tell you to keep it a 6 or change it to a 7?)
If it is five or more, add one more.
35.62 rounded to the nearest whole number is 35.6.
Example 3 Real-World Example
SODA A bottle of soda costs $0.058 per fluid ounce. How much is this to the nearest cent?
0.058
To the nearest cent, the cost is $0.06 per fluid ounce
Lesson 3-4: Estimating Sums and Differences
Example 1 Use Rounding to Solve Problems
FAST FOOD Estimate the total number of sandwiches sold weekly if 32.5 thousand burgers are sold and 18.3 thousand chicken sandwiches are sold.
Round each number to the nearest ten for easier adding.
32.5 → 3032.5 rounds to 30.
+ 18.3 → + 2018.3 rounds to 20.
50
There are about 50 thousand sandwiches sold per week.
Year / Snowfall (in.)2002 / 19.5
2003 / 20.6
2004 / 18.9
2005 / 20.4
Example 2 Use Clustering to Solve Problems
The table shows the number of inches of snow in a city for each year. Use clustering to estimate the total amount of snowfall for the four years?
The addends are clustered around 20. Round each decimal to 20.
19.5→20
20.6→20
18.9→20
20.4→ 20
Multiplication is repeated addition. So, a good estimate of the total snowfall for the four years is 4 20, or 80.
Example 4 Use Front-End Estimation
Estimate 42.5 + 31.3 using front-end estimation.
42.5→ 40.0Add the front digits.
+ 31.3→+ 30.0
70.0
Using front-end estimation, 42.5 + 31.3 is about 70.0.
Chapter 3: Lessons 3-5 to 3-9
STUDY GUIDE
This study guide provides you with an overview of the types of problems and skills that we will learn or have learned in the lessons listed above. In addition to this guide, review the Lesson 3-1 to 3-4 guide, your step by step notes for each lesson, and we will complete additional review problems in class, as we get closer to the test.
Lesson 3-5: Adding and Subtracting Decimals
Example 1 Add Decimals
Find the sum of 53.6 and 25.1.
Estimate53.6 + 25.1 ≈ 54 + 25 or 79
53.6Line up the decimal points.
+ 25.1
78.7Add as with whole numbers.
The sum of 53.6 and 25.1 is 78.7.
Example 2 Subtract Decimals
Find 9.537 – 5.315.
Estimate9.537 − 5.315 ≈ 10 − 5 or 5
9.537Line up the decimal points.
− 5.315
4.222Subtract as with whole numbers.
So, 9.537 − 5.315 = 4.222Check for Reasonableness 4.222 ≈ 5
Example 3 Annex Zeros
Find 8 – 3.54.
Estimate8 − 3.54 ≈ 8 − 4 or 4
8.00Annex zeros so that both numbers have the same place value.
−3.54
4.46
So, 8 – 3.54 = 4.46.Check for Reasonableness 4.46 ≈ 4
Example 4 Real-World Example
VACATION The price of a hotel room at a popular vacation resort is $179.95 per night. At a hotel just outside the resort, the price of a room is $124.50 per night. What is the difference between these two prices?
Estimate$179.95 − $124.50 ≈ $180 − $125 or $55
$179.95Line up the decimal points.
− $124.50
$55.45Subtract as with whole numbers.
So, the hotel on the grounds of the vacation resort is $55.45 more than the hotel outside of the resort. Check for Reasonableness $55.45 ≈ $55
Example 5 Evaluate an Expression
ALGEBRA Evaluate c – d if c = 23.64 and d = 7.31.
c − d = 23.64 − 7.31 Replace c with 23.64 and d with 7.31.
Estimate23.64 − 7.31 ≈ 24 − 7 or 17
23.64Line up the decimal points.
− 7.31
16.33Subtract as with whole numbers.
The value is 16.33.
Check for Reasonableness 16.33 ≈ 17
Lesson 3-6: Multiplying Decimals by Whole Numbers
Example 1 Multiply Decimals
Find 15.3 4.
2 1
15.3
4
61.2
Example 2 Multiply Decimals
Find 7 0.72.
5 1
0.72
7
5.04
Example 3 Annex Zeros in the Product
Find 6 0.013.
1
0.013
6
0.078
Example 4 Multiply by 10, 100, or 1,000
Find 8.2 × 1,000.
METHOD 1 Use paper and pencil.
1,000
8.2one decimal place
2000
80000
8,200.0one decimal place
OR
METHOD 2 Use mental math.
Move the decimal point to the right the same number of zeros that are in 1,000, or 3 places.
8.2 × 1000 = 8.200 or 8,200
Lesson 3-7: Multiplying Decimals
Example 1 Multiply Decimals
Find 3.8 5.2.Estimate 3.8 5.2 → 4 5 or 20
3.8 one decimal place
5.2 one decimal place
76
1900
19.76 two decimal places
The product is 19.76.Compared to the estimate, the product is reasonable.
Example 2 Multiply Decimals
Find 2.3 0.04.Estimate 2.3 0.04 → 2 0 or 0
2.3 one decimal place
0.04 two decimal places
0.092 three decimal places
The product is 0.092.Compared to the estimate, the product is reasonable.
Example 3 Real-World Example
INCOME Josephine works at a job where she earns $7.40 per hour. How much would her paycheck be for a week in which she works 26.25 hours?
Estimate 26.25 7.40 → 26 7 or 182
26.25 two decimal places
7.40 two decimal places
0000
105000
1837500
194.2500
Josephine’s paycheck would be $194.25.
Lesson 3-8: Dividing Decimals by Whole Numbers
Example 1 Divide a Decimal by a 1-Digit Number
Find 9.6 3.Estimate 9 3 = 3
3
− 9
0 6
− 6
09.6 3 = 3.2 Compared to the estimate, the quotient is reasonable.
Example 2 Divide a Decimal by a 2-Digit Number
Find 5.4 12. Estimate 5 10 = 0.5
0.45
12 5.40
− 4 8
60
− 60
0
5.4 12 = 0.45 Compared to the estimate, the quotient is reasonable.
Lesson 3-9: Dividing by Decimals
Example 1 Divide by Decimals
Find 6.93 1.8. Estimate 7 2 = 3.5
Multiply both the divisor and the dividend by 10 to make the divisor a whole number.
1.8Place the decimal point.
− 54Divide as with whole numbers.
153
− 144
90Annex a zero to continue.
− 90
0
6.93 divided by 1.8 is 3.85.Compare to the estimate.
Check3.85 × 1.8 = 6.93
Example 2 Divide by Decimals
Find 4.09 0.02