Math 5
Unit 1
Lesson 6
Parts of a Whole - Decimals
Canada Geese
Canada Geese can be identified by their long black
neck, black head, crown and bill. The back and
feathers on top of their wings are shades of
brown. The throat, cheeks, and under-tail of the
bird are white. These white marks make it easy
to identify them.
Canada geese travel in large groups and fly in a
V-shaped formation. They may migrate in the
winter to parts of the United States.
They are a rather large bird. They range from 0.508 to 1.270 metres in
length. They can have a wingspan of 1.270 to 1.272 metres.
Reflection
How do you say 0.508? What fraction of a
metre is 0.508?
Math 5
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Math 5
Unit 1
Lesson 6: Parts of a Whole - Decimals
Objectives for this Lesson
In this lesson you will explore the following concepts:
• Describe and represent decimals concretely, pictorially
and symbolically
• Relate decimals to fractions
Go online to complete the Concept Capsule: Understanding
Decimals Using Base 10 Blocks.
Parts of a Whole
Remember that one way to show a picture of a decimal is to use base ten
blocks. Since those are hard to put on paper they may be represented
with these pictures:
1-62
Three Tenths or 0.3
Three Hundredths or 0.03
The square has 10 parts.
3 parts are shaded.
The 3 goes in the tenths place.
The square has 100 parts.
3 parts are shaded.
The 3 goes in the hundredths place.
Ones
.
Tenths
0
•
3
Hundredths Thousandths
Ones
.
Tenths
0
•
0
Hundredths Thousandths
3
Math 5
Unit 1
Lesson 6: Parts of a Whole - Decimals
Now It’s Your Turn
Write the decimal to match the shaded part of each picture.
a.
b.
c.
b. 0.64
c. 0.46
Solutions
a. 0.6
Relate Fractions to Decimals
Fractions and decimals both relate parts to a whole. Decimals always
have a whole that is cut into 10, 100, 1 000, and so on.
Fractions may have any number of parts.
1
2
3
10
5
8
9
100
When you look at models of fractions you can see that they may also
represent decimals.
Math 5
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Math 5
Unit 1
Lesson 6: Parts of a Whole - Decimals
For the following, notice the decimal and the fraction:
Picture
Parts of Whole
Decimal
Fraction
There are 76
shaded parts of
the whole that is
divided into 100
pieces.
0.76
76
100
The number of shaded parts follows the decimal place. The last digit is in
the hundredths place because there are 100 parts to the whole. If there
were 10 parts then the last place would fall in the tenths place.
For the fraction, the numerator is the number of shaded parts. The
denominator is 100 because there are 100 parts to the whole.
Example 1
For the picture shown, answer the following questions:
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A. What decimal amount is shaded?
B. What fractional amount is shaded?
Math 5
Unit 1
Lesson 6: Parts of a Whole - Decimals
A.How many parts are in the whole? Remember, this will tell you the
place value of your decimal.
There are 10 parts. The decimal will have a tenths place: 0.___
How many parts are shaded? This will be the number in the tenths place.
4 parts are shaded.
The decimal amount shaded is: 0.4
B.How many parts are in the whole? Remember, this will tell you the
number in the denominator.
There are 10 parts. The fraction will have a 10 in the denominator:
4
10
How many parts are shaded? This will be the number in the
numerator.
4 parts are shaded.
The fraction will be:
4
10
Example 2
For the picture shown, answer the following questions:
A. What decimal amount is shaded?
B. What fractional amount is shaded?
Math 5
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Math 5
Unit 1
Lesson 6: Parts of a Whole - Decimals
A.How many parts are in the whole? Remember, this will tell you the
place value of your decimal.
There are 100 parts. The decimal will have a hundredths place:
0. ___ ___
How many parts are shaded? This will be the number in the tenths place.
49 parts are shaded.
The decimal will be: 0.49
B.How many parts are in the whole? Remember, this will tell you the
number in the denominator.
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49
There are 100 parts. The fraction will have a 100 in the denominator: 100
How many parts are shaded? This will be the number in the numerator.
49 parts are shaded.
The fraction will be: 100
49
Math 5
Unit 1
Lesson 6: Parts of a Whole - Decimals
Let’s Explore
Exploration 1: Fraction – Decimal Patterns
Materials: Unit 1, Lesson 6, Exploration 1 page from your Workbook, Pencil
Notice the pattern to the table of equivalent fractions and decimals:
Fraction
3
10
6
10
7
10
9
10
4
100
23
100
30
100
68
100
Decimal
0.3
0.6
0.7
0.9
0.04
0.23
0.30
0.68
1. What do you notice about the decimals when the denominator is 10?
2.What do you notice about the decimals when the fraction’s
denominator is 100?
3.Reflect: What is the relationship between the denominator of the
fraction and the place value of the decimal?
4. Apply this knowledge: Complete the table.
Fraction
Decimal
Math 5
2
10
8
10
0.5
21
100
0.12
39
100
0.57
0.84
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Math 5
Unit 1
Lesson 6: Parts of a Whole - Decimals
Now It’s Your Turn
Write each decimal as a fraction.
a. 0.2
b. 0.5
c. 0.23
d. 0.06
Solutions
a. 2
10
b. 5
10
c. 23
100
d.
6
100
Let’s Practice
• In your Workbook go to Unit 1, Lesson 6 and complete 1 to 6.
Thousandths
1
Think about this pattern:0.1 = 10
,
1
0.01 = 100
Notice that the number of zeros in the denominator of the fraction is
equal to the number of decimal places in the decimal.
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Math 5
Unit 1
Lesson 6: Parts of a Whole - Decimals
What decimal value would equal
1 ? Based on the pattern you
1 000
observed, your answer should be 0.001.
Example 3
The cactus pygmy-owl is about 168 of a metre long. Write the fraction
1 000
as a decimal.
You would read the fraction like this: “one hundred sixty eight thousandths”
The denominator tells you that the 8 goes in the thousandths place.
You will put the 1 and 6 in the spaces before the 8.
Ones
.
Tenths
Hundredths
Thousandths
0
•
1
6
8
168 = 0.168
1 000
Math 5
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Math 5
Unit 1
Lesson 6: Parts of a Whole - Decimals
Example 4
Write
5
as a decimal.
1 000
You would read the fraction like this: “five one thousandths”
The denominator tells you that the 5 will be in the thousandths place.
You need to fill in the other places after the decimal with a 0.
Ones
.
Tenths
Hundredths
Thousandths
0
•
0
0
5
5
= 0.005
1000
Example 5
Write 1 14
as a decimal.
000
There are two digits in the numerator. The 4 must be placed in the
thousandths place so the 1 will be in the hundredths and a 0 in the
tenths. You must think backwards to get this one; the last digit has to be
in the thousandths place.
Ones
.
Tenths
Hundredths
Thousandths
0
•
0
1
4
14 = 0.014
1000
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Math 5
Unit 1
Lesson 6: Parts of a Whole - Decimals
Now It’s Your Turn
Write each fraction as a decimal.
a. 3
10
b. 17
100
9
c. 1 000
d. 1 32
000
Solutions
a. 0.3
b. 0.17
c. 0.009
d. 0.032
Let’s Practice
o online to watch the Notepad Tutor: Relating Decimals to Fractions
G
(to thousandths).
• In your Workbook go to Unit 1, Lesson 5 and complete 7 to 20.
Math 5
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Math 5
Unit 1
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Lesson 6: Parts of a Whole - Decimals