Download Module 4 Worksheets Module 4A –5.1 and 5.2 5.1 Decimal Notation

Module 4 Worksheets
Module 4A –5.1 and 5.2
5.1 Decimal Notation
Objective A –Given decimal notation, write a word name, and write a word name for an amount of
money
Label the place value in the number.
4 3 8
We can continue to write place value to the right of the one’s place after a decimal point.
Label the place values that occur after the decimal point:
438._________ ___________ ___________
438.752 is written in decimal notation.
How do we read this number?
How do we write a word name for decimal notation?
a)
b)
c)
Write a word name for the number in the sentence: The world record in the men’s 800 meter run is
1.6852 min, held by Wilson Kipketer of Denmark.
Write in words, as on a check: $524.95
Objective B- Convert between fraction notation and decimal notation.
3.57 stands for what?
To convert from decimal to fraction notation:
a)
b)
c)
Write 0.0109 as a fraction.
Write -2.6073 as a fraction and as a mixed number.
Fraction:
Mixed number:
To convert from fraction notation to decimal notation when the denominators are 10, 100, 1000, and so
on:
a)
b)
Convert 
9
to decimal notation.
100
Write decimal notation for 7
13
1000
Objective C – Given a pair of numbers in decimal notation, tell which is larger.
We can graph numbers on a number line. Graph 1.09 and 1.3 on the number line below.
Which number is larger? 1.3 or 1.09
1.3 ____ 1.09
How do we compare two positive numbers written in decimal notation?
Which number is larger? 0.403 or 0.410
Graph -0.15 and -0.187. Draw the number line below.
Which one is larger? -0.15_______-0.187
How do we compare two negative numbers in decimal notation?
Which number is larger? -3.8 or -3.82
-3.8 ______ -3.82
Objective D – Round decimal notation to the nearest tenth, hundredth, thousandths, or ten, hundred,
thousand
To round to a certain place:
a)
b)
c)
Round 72.3846 to the nearest hundredth.
Round -0.372 to the nearest tenth.
5.2 Addition and Subtraction of Decimals
Objective A – Add using decimal notation
What do we do when we add decimals?
Why do we line up decimals?
Add: 56.314+17.78
Add: 0.34+3.5+0.127+768
Objective B – Subtract using decimal notation
How do we subtract decimals?
Subtract: 56.314-17.78
How do we check subtraction?
Subtract: 2 – 1.0908
Objective C – Add and Subtract Negative Decimals
To add a negative number and a positive number:
a)
b)
c)
Add: 14.301 + (-17.82)
To add two negative numbers:
a)
b)
Add: -2.9 + (-4.3)
Subtract: -4.9 – 5.392
Subtract: -7.9 - (-8.5)
STOP THE VIDEO AT THIS POINT! DO NOT CONTINUE TO THE NEXT OBJECTIVE. TIME FOR 5.1 AND 5.2
HOMEWORK.
Module 4B - Multiplication of Decimals
Obj. 1 Multiply using decimal notation
Multiply 2.3 × 1.12 by converting the decimals to fractions.
What conclusion can be drawn about the number of decimal places?
Multiply 0.02 × 3.412 by converting to fractions. Does the conclusion about the number of decimal
places above hold true?
To multiply using decimals, use the following steps:
a)
b)
Multiply
6.3 X 84.7
.0032 X 2148
: 749(-0.43)
To multiply any number by a tenth, hundredth, thousandth (or so on), use the following steps:
a)
b)
Multiply by moving decimals and inserting zeros as necessary.
0.1 X 79.81
0.01 X 243.7
.001 X (-52.8)
.0001 X 61.5
To multiply any number by a power of ten, follow the following steps:
a)
b)
Multiply by moving decimals and inserting zeros as necessary.
10 X 42.63
-7.8 X 100
1000 X (-2.4167)
10,000 X 9.51
Obj. 2 Convert between dollars and cents and convert words names
1) How many decimals places do you move for each of the following?
a) hundred
b) thousand
c) million
d) billion
e) trillion
2) How do you write 67.3 million in standard notation?
3) How do you convert from dollars to cents?
4) Convert to cents.
$189.64
$0.66
5) How do you convert from cents to dollars?
6) Convert to dollars.
783₵
4205₵
STOP THE VIDEO AT THIS POINT!!! DO NOT CONTINUE TO THE NEXT OBJECTIVE. Go to homework 5.3.
Module 4C - Division of Decimals
Obj. 1 Divide using decimal notation
1) The number of decimal places in the quotient is always equal to the number of decimal places in the
____________?
To divide by a whole number, follow the following steps:
a)
b)
2) Divide
3) a) If you don’t have a decimal point you must add it at the __________________ of the number.
b) Divide: 5 82
4) To divide by a non-whole number, follow the following steps:
a)
b)
5)
6) What is quick method for dividing by a power of 10?
a)
b)
7) Divide:
 213.4567
100
STOP THE VIDEO AND ANSWER THE FOLLOWING QUESTION. CONTINUE WITH THE VIDEO AFTER THE
QUESTION IS ANSWERED:
8) How many places and in what direction would you move the decimal when dividing by 10000?
9) To divide by a tenth, hundred, or thousand, we follow the same steps as above except instead we
move the decimal which direction?
10) Divide:
1.0237
0.001
STOP THE VIDEO AT THIS POINT!!!! DO NOT GO ON TO THE NEXT OBJECTIVE Go to homework 5.4.
Module 4D 5.5, 6.2, 6.3
5.5 More with Fractions and Decimal Notation
Objective A – Convert Fractions to Decimal
You can use ______________________________ to convert from fraction notation to decimal notation.
One way to explain how to properly set up your division problems has been described as using the
dumptruck. Think of a dump truck. The truck is on the bottom and the load is on the top (just like the
denominator is on the bottom of a fraction and the numerator is on the top. Now think of the long
division symbol as the hole being filled by the dumptruck. The truck stays outside the hole and the load
falls in the hole.
The fraction
7
can also be written as :
8
Using the long division symbol, find the decimal equivalent to
7
.
8
What is a terminating decimal? What is a repeating decimal?
Find the decimal equivalent for
4
. What is strange about the result?
11
Where does the bar go in a repeating decimal?
Obj. 2 Round decimal notation
Find the decimal equivalent for
7
.
12
Write the answer in a short-hand way (with the appropriate bar):
Write the answer without using a bar. Why might we want to do this when rounding?
1) Round to the nearest tenth
2) Round to the nearest hundredth
3) Round to the nearest thousandth
Obj. 3 Converting fractions to decimal
We can use _______________ ___________________ to convert from fraction notation to decimal
notation.
Convert directly to decimal without dividing
7

4
=
For what denominators are you able to convert without explicitly dividing?
Obj. 4 Simplify an expression with both fraction and decimal notation
Calculate
47
 79.95) 
9
Why is it not a good idea to convert the fraction to a decimal in the above problem?
6.2 Percent Notation
Obj. 1 Three kinds of notation for percent
What are the three kinds of notation for percent?
Write three kinds of notation for 27.5%
Obj. 2 Convert between decimal and percent notation
Find decimal notation for 45.6%
What effect does multiplying by .01 have on the number being multiplied?
To convert from percent notation to decimal notation use the following steps:
a)
b)
Find decimal notation for .18%
Find decimal notation for 700%
When a decimal is not shown where do you put it?
Find percent notation for .03
To convert from decimal notation to percent notation use the following steps:
a)
b)
Find percent notation for .017
6.3 Percent and Fraction Notation
Obj. 1 Convert fraction notation to percent notation
Can you go always go straight from fraction notation to percent notation? __________
What do you need to do first? ______________________________________________
Convert
13
to percent notation.
16
When you convert
Convert
2
to a decimal, what kind of decimal is it?
3
2
to percent notation.
3
Why is it quicker to convert
Convert
17
to a percent than the previous problems?
20
17
to a percent. Show work.
20
Obj. 2 Convert percent to fraction notation
Find fraction notation for 62.5%
Write fraction notation for 16. 6 %
Module 4E – 6.4 and 16.3
6.4 - Solving percent problems using percent equations
Objective 1. Translate percent problems to percent equations
Key words in percent translations:
“Of”
translates to
_____________________________
“is”
translates to
_____________________________
“What”
translates to
_____________________________
“%”
translates to
_____________________________
Examples:
Translate this problem to equation:
1) What is 32% of 78?
2) 13 is 25% of what?
STOP THE VIDEO AND ANSWER THE FOLLOWING QUESTIONS. CONTINUE WITH THE VIDEO AFTER THE
QUESTIONS ARE ANSWERED:
When translating to a percent equation, you must write the percent in decimal notation using the
"X 0.01" rule. So, in the above example, 32% should be written as 32 X 0.01 or .32. How should 25% be
written?
Write each of the equations above using decimal notation in place of percent notation:
1)
2)
Objective 2. Solve basic percent problems
Types of percent problems:
1. Finding the _____________________________________ (result of taking percent)
Solve:
What is 6% of $300?
2. Finding the ______________________________________ (number you are taking percent of)
Solve:
56.32 is 64% of what?
3. Finding the ______________________________________ (the percent itself)
Solve:
What percent of $50 is $16?
16.3 Simplify Square Roots of Perfect Squares of Decimals
List the steps for simplifying square roots of decimals and work the examples with the video.
Example 1:
.0016 (This first example will be worked out as the steps are explained.)
1.
2.
3.
4.
Example 2:
.000064