Name:_____________________Chapter 2 Test Date:______
Chapter 2: Decimals
Lesson 2.1 Understanding Decimals
Objective: Read and write numbers through the hundred-thousandths.
Warm-Up: Identify the place and value of the underlined digit.
1. 3,003,158
__________________;__________________
2. 47,890,256
__________________;__________________
3. 5,017,903
__________________;__________________
4. 79,522,008
__________________;__________________
A decimal is a number that uses a decimal point.
***decimal place value chart
The place-value system can be extended to include numbers between whole
numbers.
What are some ways to read and write decimals?
How do you read and write 1.00797?
Standard form: 1.00797
Word form: One and seven hundred ninety-seven
hundred-thousandths
Short-word form: 1 and 797 hundred-thousandths
Expanded form: 1 + 0.007 + 0.0009 + 0.00007
Practice Problems:
1. Use the place-value chart to find the place and value of each digit in the
decimal 0.53482.
5 = __________________;__________________
3 = __________________;__________________
4 = __________________;__________________
8 = __________________;__________________
2 = __________________;__________________
2. One way to read a decimal is to say it as you would a fraction or mixed
number. How would you write 55.847 as a mixed number? ______________
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3. Give the place and value of 7 in each number.
1. 34.798 __________________;__________________
2. 0.07964__________________;_________________
3. 45.62173_________________;__________________
4. Complete the table.
Standard Form
Short-Word Form
1.3506
Expanded Form
1 + 0.3 + 0.05 + 0.0006
204 thousandths
0.5402
3 and 897 hundredthousandths
Something to think about:
1. Justify the importance of decimals in our lives.
_________________________________________________________
_________________________________________________________
2. What conclusions can you draw about reading numbers in decimal place
value? ____________________________________________________
_________________________________________________________
_________________________________________________________
3. Explain the importance of decimal place value. ____________________
_________________________________________________________
_________________________________________________________
4. Why are there no oneths in decimal place value?___________________
_________________________________________________________
_________________________________________________________
Lesson 2.2 Comparing and Ordering Decimals
Objective: Compare two decimals using <,> or =; order three or more decimals.
Warm-Up: Use < or > to compare.
1. 4,895
_____
4,859
2. 56,532 _____
56,498
Order these from least to greatest.
6,010; 6110; 6,101; ______________;______________;_____________
92,055; 95,022; 95,052 _____________;____________;____________
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You can compare and order decimals in several ways.
1. One way is to compare and order decimals is to locate them on a
number line.
____________________________
2. A second way is to align the digits by place value. Annexing (adding zeros
on the end of the number) can help you do this. This does not change t he
value of a number.
Compare 2.24 and 2.2
2.24
2.2__
**Start at the left and compare digits in the same place value.
Practice Problems: Compare each pair of numbers.
1. 0.0567 _____
0.0499
2. 1.45
_____
0.001
3. 17.003
_____
0.0135
_____
17.030
4. 0.135
Order each group of numbers from least to greatest.
5. 639.087; 639.078; 638.088
__________________________
__________________________
__________________________
6. 105.65; 0.328; 10.565; 0.001
__________________________
__________________________
__________________________
__________________________
Something to think about:
1. Identify the strategies to use when comparing numbers with decimal
place value. ________________________________________________
_________________________________________________________
_________________________________________________________
2. What conclusions can you draw about ordering numbers with decimal place
value? ____________________________________________________
_________________________________________________________
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3. Explain the importance of comparing and ordering decimals. _________
_________________________________________________________
_________________________________________________________
Lesson 2.3 Rounding Decimals
Objective: Round decimals to a specified place.
Warm-Up: Identify the place and value of each 4.
1. 5.0649 ____________________;_____________________
2. 48.621
____________________;____________________
3. 0.458
____________________;_____________________
4. 22.345 ____________________;_____________________
Use these four steps to round decimal numbers:
1. Find the rounding place and underline that digit.
2. Look at the digit to the right of this underlined place and circle
that digit.
3. If the circled digit is less than < 5 (0-4) leave the underlined digit
the same. (4 or below leave it alone)
4. If the circled digit is greater than > or = to 5 round the
underlined digit up one number. (5 or above give it a shove)
5. Change all digits to the right of the underlined digit (rounding
digit) to zeros.
6. Drop any digits following the rounded place to the right of the
decimal.
Round to the nearest tenth:
4.08765
________________
28.16597
________________
3.1042
14.199
________________
________________
Round to the nearest hundredth:
4.08765
________________
28.16597
________________
313.1042
14.199
________________
________________
Round to the nearest hundred-thousandths:
4.0876567 ________________
313.1042001 _______________
28.16597
________________
14.19999
________________
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2.4 Estimating with Decimals
Objective: Estimate sums, differences, products, and quotients of decimals
using rounding and compatible numbers.
** You can estimate with decimals using the same methods as whole
numbers.(Lessons 1.5 and 1.6 notes)
Warm-Up: Estimate
1. 27,802 + 368 ≈ ____________________
2. 1,298 – 99 ≈ ______________________
3. 403 ÷ 79 ≈ _______________________
4. 5100 x 162 ≈ ______________________
The symbol ≈ means “is approximately equal to.”
Read over examples on page 82 in textbook.
Practice Problems: Estimate the answer.
1. 95.89 + 12.02 ≈ _____________________
2. 70.508 ÷ 8.4 ≈ _____________________
3. 48.53 x 3.8 ≈ ______________________
4. 75.361 – 29.499 ≈ ___________________
Something to think about:
1. Describe in your own words what estimating sums, differences, products
and quotients.______________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
2. How would you compare rounding and estimating whole numbers to
rounding and estimating decimals? _______________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
3. Describe decimal place value in your own words. __________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
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Lesson 2.5 Adding and Subtracting Decimals
Objective: Add and subtract whole numbers and decimals of varying place
values.
Warm-Up: Estimate
1. 80.5 + 502 + 102.3 ≈ ____________________
2. 6289.876 – 285.499 ≈ __________________
3. 8.693 – 4.536 ≈ _______________________
4. 0.197 + 1.16 ≈ _________________________
Rule: Line up the decimal points.
A. Arrange the numbers so the decimal points form a straight column.
B. Add or subtract.
C. Place a decimal in the answer so it lines up with the column of decimals.
hundreds
tens
ones
decimal
point
tenths
hundredths
thousandths
tenthousandths
•
•
•
•
•
•
•
•
•
•
•
Practice Problems:
1. 1.8 + 0.78 =
_+_________________
2. 1.8 – 0.78 =
-________________
3. 45.6 + 26.3 =
_+_________________
4. 84.84 – 22.7 =
-________________
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5. 26.9 + 3.82 + 114 + 2.705 =
6. 52.5 – 23.632 =
Something to think about:
1. State the “rule” for adding and subtracting decimals. _______________
_________________________________________________________
_________________________________________________________
2. Justify why this rule is so important. Support your answer with details.
_________________________________________________________
_________________________________________________________
_________________________________________________________
Lesson 2.6 Multiplying Whole Numbers and Decimals
Objective: Multiply whole numbers and decimals.
Warm-Up: Estimate
1. 5.89 x 3.02 ≈ _____________________
2. 725 x 4 ≈ _______________________
3. 173 x 9.9 ≈ ______________________
Rule: Count the decimal places.
A. Multiply as usual.
B. COUNT the total number of decimal places in both factors.
C. Start at the right of the product, then move the decimal to the left
the total number of decimals places in both factors.
D. Sometimes you need to annex (add/place) zeros to the left of the
product to place the decimal correctly.
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Practice Problems:
1. 3.8 x 5.7 =
2. 7.12 x 3.54 =
3. 9.017 x 6.333=
4. 27.8 x 13.2 =
5. 518.43 x 28.563=
6. 7395.8 x 49.83=
Something to think about:
1. How do you know where to place the decimal when multiplying decimals?
_________________________________________________________
_________________________________________________________
_________________________________________________________
2. What would happen to the product if one factor with 3 decimal places is
multiplied by another factor with 2 decimal places? How many decimal
places would be in the product? Defend your answer with details.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Lesson 2.7 Dividing By Whole Numbers
Objective: Divide whole numbers and decimals by a whole number.
Warm-Up: Estimate
1. 831 ÷ 41 ≈ ____________________
2. 15.9 ÷ 8 ≈ ____________________
3. 6.38 ÷ 2.3 ≈ ___________________
4. 100.6 ÷ 10.7 ≈__________________
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Rule: Divide as usual and place the decimal straight up from
the dividend to the quotient.
Example:
A. Line up the decimal in the answer with the decimal in the dividend.
B. Divide as usual.
Dividing Tips:
G/D=guess or divide
M=multiply
S=subtract
C=check
B=bring down the next #
Grandma Makes Such Crumby Bread
Hint: The decimal is always there. If you don’t see it…the decimal point is
located directly to the right of the ones place.
Three ways to write division problems:
1.
2.
3.
Practice Problems:
1. 20.7 ÷ 9 =
2. 77 ÷ 4 =
3. 130 ÷ 1000
4. 961.23 ÷ 13 =
Something to think about:
1. Identify the rule and the steps needed to divide into a decimal.
_________________________________________________________
_________________________________________________________
_________________________________________________________
2. Compare and contrast dividing decimals with multiplying decimals. (Venn)
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Lesson 2.8 Interpreting Remainders
Objective: Interpret remainders when solving division problems.
Problem-Solving Skill: When you solve a word problem using division, the
real-world situation to make sense of the answer. Use common sense.
Go over workbook page 25 on the front.
Lesson 2.9 Dividing By a Decimal
Objective: Divide whole numbers and decimals by decimals.
Warm-Up: Find the quotient.
1. 80.6 ÷ 26 =
2. 29 ÷ 4 =
3. 0.48 ÷ 32 =
Rule: Move the decimal in the divisor. Then move the
decimal point that many times in the dividend. Then place it in
the quotient.
A. Count the number of decimal places in the divisor.
B. Count the same number of places after the decimal in
the dividend.
C. Line up the decimal in the quotient with the “new” spot in the dividend.
D. Divide as usual.
Practice Problems:
1. 120.6 ÷ 6.7 =
2. 1.8 ÷ 6.3 =
3. 2.32 ÷ .93=
4. 0.36 ÷ 126 =
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Something to think about:
1. What would result if the decimal point in the divisor was not moved?
_________________________________________________________
_________________________________________________________
_________________________________________________________
2. Identify the rule for dividing by a decimal._______________________
_________________________________________________________
_________________________________________________________
3. Explain the rules for dividing once the decimals are properly moved.
________________________________________________________________________
________________________________________________________________________
Lesson 2.12 Solving Equations with Decimals
Objective: Solve one-step linear equations involving decimals.
Warm-Up: Solve and Check.
1. 15x = 105
2. 22 + y = 50
3. a ÷ 5 = 35
4. n – 33 = 3
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Steps to Solving Equations with Decimals:
1. Locate the side of the equation with the variable and determine the
operation being used.
2. Use the inverse operation on the side with the variable.
The inverse of addition is subtraction.
The inverse of subtraction is addition.
The inverse of multiplication is division.
The inverse of division is multiplication.
3. Use the properties of equality to balance the equation. Whatever you do
to one side of the equation you must do to the other side of the
equation. Keep the balance!
4. Solve the equation to find out the answer to the variable.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Steps for Checking your Algebraic Equations:
*** The check must be written as follows:
Check:
F
1. Write the original formula/equation.
S
2. Substitute the value of the variable for the variable. Prove it by
doing the work.
S
3. Solve…check to make sure the equation is =.
Practice Problems:
1. m + 0.6 = 3
Check:
1.
2.
3.
2. w – 4.2 = 8.2
Check:
1.
2.
3.
3. 6.9 = 2.3h
Check:
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4. m ÷ 1.6 = 6
Check:
Something to think about:
1. What is the most important part of solving equations with decimals?
_________________________________________________________
_________________________________________________________
2. How do you evaluate algebraic equations with decimals?_____________
_________________________________________________________
_________________________________________________________
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