Answer Key • Lesson 3: Many Ways to Show Decimals
Student Guide
Many Ways to Show Decimals
(SG pp. 368–374)
Questions 1–12
1.
Many Ways to Show Decimals
Hundredths on Grids
In an art class, Frank used colored tiles to make a mosaic using a 10 ⫻ 10 grid. He
used a data table to keep track of the number of tiles he used for each color.
Number of Each Color
Color
Number of Tiles
blue
30
green
12
yellow
32
red
20
orange
6
Common
Fraction
Decimal
Fraction
30
—
—
100
12
—
—
100
.30
thirty hundredths
.12
twelve hundredths
32
—
—
100
20
—
—
100
.32
thirty-two hundredths
red
.20
twenty hundredths
orange
—6—
100
.60
sixty hundredths
Color
blue
gree
yellow
1. Make a chart to show what fraction of the grid is colored by each color.
Write a common fraction, decimal fraction, and words in a chart.
Decimal
Fraction
Number in Words
30
—
—
100
.30
thirty hundredths
Mr. Moreno displayed a 10 ⫻ 10 grid that
was partially shaded and asked the
students to decide how much of the grid
was shaded.
Lee Yah’s group wrote 0.84 as their
answer.
Copyright © Kendall Hunt Publishing Company
Color
blue
Common
Fraction
84 .
Michael’group wrote ⫺
⫺
100
Nila’s group wrote 0.8 ⫹ 0.04 as their
response, and Ming’s group wrote
eighty-four hundredths as their answer.
2. Mr. Moreno said that they were all correct. Explain how each answer can be
correct.
368
SG • Grade 5 • Unit 8 • Lesson 3
Many Ways to Show Decimals
Student Guide - Page 368
Number in Words
2.* All three answers are correct because they all
represent the part of the grid that is shaded.
There are 100 small boxes and 84 are shaded,
84
. In the decimal notation, it shows
so that is 100
1
that the whole is divided into pieces that are 10
the size of the whole. Nila’s group saw the
1
8 rows that are each 10 of the whole and
1
of the whole. Nila’s
4 boxes that are each 100
group is using expanded form.
3. A. 10
B. 100
C. 1000
Use the Decimal Grids: Hundredths pages in the Student Activity Book to practice
representing decimals.
Thousandths on Grids
B. How many tiny rectangles are there in one row of small squares?
Copyright © Kendall Hunt Publishing Company
C.
How many tiny rectangles are there in one whole grid?
1
Each tiny rectangle represents one-thousandths ( ⫺
⫺) of the whole. This is
1000
written 0.001 as a decimal. Grids like this can be used to model thousandths.
Many Ways to Show Decimals
SG • Grade 5 • Unit 8 • Lesson 3
369
Student Guide - Page 369
*Answers and/or discussion are included in the lesson.
1
TG • Grade 5 • Unit 8 • Lesson 3 • Answer Key
Copyright © Kendall Hunt Publishing Company
3. A. Mr. Moreno divided each square in the 10 ⫻ 10 grid into tiny rectangles.
How many tiny rectangles are in each small square?
Answer Key • Lesson 3: Many Ways to Show Decimals
This grid models 0.357 (three-hundred fifty-seven thousandths).
4. A. How many rows are fully shaded on this grid? Write a decimal to
represent the fully shaded rows.
B. How many squares are in the fully shaded rows? Write a decimal to
represent the number of squares in these rows.
C. How many tiny rectangles are in the fully shaded rows? Write a decimal
to represent the number of tiny rectangles in these rows.
D. Look at the row that is partially shaded. How many squares are shaded
in this row? Write a decimal to represent the number of squares that are
shaded in this row.
E. How many extra tiny rectangles are shaded in this row? Write a decimal
to represent the extra tiny rectangles that are shaded in this row.
F. Write a number sentence in expanded form to show 0.357.
⫹ 0.05 ⫹
⫽ 0.357
Jackie and Linda decided to use Grace’s strategy to place 0.357 on a number line.
Jackie knows that 0.357 is between 0.3 and 0.4 but if she uses tenths she will
need to divide the number line into 100 small parts to find the location of 0.357.
5. A. Linda suggests using hundredths to label the ends of the number line.
Between which two hundredths is 0.357 located?
Copyright © Kendall Hunt Publishing Company
4. A.* 3 full rows are shaded or 0.3 or three tenths
of the grid is shaded.
B.* 30 squares; 0.30 or thirty hundredths of the
grid is shaded.
C.* 300 tiny rectangles or 0.300 or
three hundred thousandths of the grid
is shaded.
D.* five squares are shaded; 0.05 or
five hundredths of the grid is shaded.
E.* 7 more tiny rectangles; .007 or
seven thousandths of the grid is shaded.
F.* .3 + .05 + .007 = 0.357
5. A.* Between .35 and .36
B.* Point A represents 0.357.
6. A.* 0.083 or eighty-three thousandths
B.* Point B represents 0.083
7. A. Grid A: 0.642; .6 + .04 + .002 = .642
Grid B: 0.649; .6 + .04 + .009 = .649
B. Grid A: six hundred forty-two thousandths
Grid B: six hundred forty-nine thousandths
C.* Both Points A represent 0.642.
Both Points B represent 0.649.
B. Which point represents the location of 0.357?
B
C
A
.35
370
.36
SG • Grade 5 • Unit 8 • Lesson 3
Many Ways to Show Decimals
Student Guide - Page 370
B. Use words to describe what fraction of each is shaded.
6. A. What fraction of the grid is shaded? Write a decimal fraction.
C. Which points represent the locations of the decimal fractions?
A
B
0.6
0.7
A
B
.64
.65
Between which two hundredths
will these decimals be?
B. Which point represents the location of the decimal fraction in
Question 6A?
Decimals with Base-Ten Pieces
.80
Jacob put some base ten pieces on his desk. He challenged his friends to guess
the number his pieces represented.
.90
Copyright © Kendall Hunt Publishing Company
B
.08
C
.09
.08
.09
7. A. What fraction of each grid is shaded? Write a decimal fraction and a
number sentence in expanded form.
Grid A
Grid B
I think the number
is 4,376.
It could be four
hundred thirty-seven
and six tenths.
Fern
Many Ways to Show Decimals
SG • Grade 5 • Unit 8 • Lesson 3
372
371
SG • Grade 5 • Unit 8 • Lesson 3
I am pretty sure
the number is
43.76.
Copyright © Kendall Hunt Publishing Company
Copyright © Kendall Hunt Publishing Company
A
I think this is a
trick question. We
don’t have enough
information to
answer.
Many Ways to Show Decimals
Student Guide - Page 372
Student Guide - Page 371
*Answers and/or discussion are included in the lesson.
TG • Grade 5 • Unit 8 • Lesson 3 • Answer Key 2
Answer Key • Lesson 3: Many Ways to Show Decimals
8. A.
8. Use base ten pieces or base ten shorthand to show each number.
A. 2469
B. 45.75
D. 280.4
E. 8.34
C. 4.503
F. Explain how the value of the digit 4 changes in the numbers in
Questions A–E.
B.
Ana put some base ten pieces on her desk.
C.
She read her number as eight and five hundred and nineteen thousandths.
.
.
Irma used base ten shorthand and a place value chart to show the value of Ana’s
pieces.
Ones
Tenths
Hundredths
D.
Thousandths
.
Copyright © Kendall Hunt Publishing Company
Luis showed Ana’s number using expanded form
8 ⫹ .5 ⫹ .01 ⫹ .009
9. A. How is Irma’s place value chart similar to Luis’s expanded form? How
are they different?
B. Write the value of Ana’s base ten pieces in standard form.
10. Write each number using expanded form.
A. 5.905
B. 7.009
D. 2.222
E. 23.528
C. 3.664
F. six and one hundred sixty-four thousandths
G. Write the number in Question 10C using words.
Many Ways to Show Decimals
Student Guide - Page 373
373
.
F.* If you line the numbers up on the place
value chart from largest to smallest, you
can see that each time the 4 moves a place
1
to the right it is 10 the value it was in the
place to the left. If you move from the
smallest number to the largest number,
each time you move the 4 a place to the left
it gets 10 times larger.
9. A. Possible response: Both the place value
chart and expanded form break the number
apart using the place value of each number.
Irma uses models to show the value of each
digit and Luis uses symbols. Irma arranged
the base-ten shorthand on a chart and Luis
put the digits into a number sentence.
B. 8.519
10. A. 5.905= 5 + .9 + .005
B. 7.009 = 7 + .009
C. 3.664 = 3 + .6 + .06 + .004
D. 2.222 = 2 + .2 + .02 + .002
E. 23.528 = 23 + .5 + .02 + .008
F. 6 + .1 + .06 + .004
G. three and six hundred sixty four thousandths
TG • Grade 5 • Unit 8 • Lesson 3 • Answer Key
Copyright © Kendall Hunt Publishing Company
3
SG • Grade 5 • Unit 8 • Lesson 3
E.
Answer Key • Lesson 3: Many Ways to Show Decimals
11. A.
B.
C.
D.
E.
F.
12.
34.308
742.091
16.945
500.043
249.613
five hundred and forty-three thousandths
Thousands
Hundreds
Tens
Ones
11. Write each number in standard form.

A. 30 ⫹ 4 ⫹ .3 ⫹ .008
B. 700 ⫹ 40 ⫹ 2 ⫹ .09 ⫹ .001
C. 10 ⫹ 6 ⫹ .9 ⫹ .04 ⫹ .005
D. 500 ⫹ .04 ⫹.003
E. Two hundred forty-nine and six hundred thirteen thousandths
F. Write the number in Question 11D using words.
Check-In: Question 12
12. Mr. Moreno used base ten pieces to display a number. Complete the place
value chart using base ten shorthand. Write the number for each
representation or represent the number with base-ten shorthand.
Tenths Hundredths Thousandths Numbers
A.
Thousands
6,183
Hundreds
Tens
Ones
Tenths Hundredths Thousandths Numbers
A.
?
B.
6.183
6.183
C.
C.
681.3
?
D.
D.
Copyright © Kendall Hunt Publishing Company
B.
?
61.83
Complete the Show Decimals pages in the Student Activity Book for more practice
representing decimals in many ways.
374
SG • Grade 5 • Unit 8 • Lesson 3
Many Ways to Show Decimals
Student Guide - Page 374
Copyright © Kendall Hunt Publishing Company
E. Possible response: In the number 613.3 the
six is worth 6 100 or 600. In the number
61.83 the six is worth 6 10 or 60. That
means that when the six moved one place to
the right from the hundreds place to the tens
1
place it is worth 10 as much.
F. Explain how the value of the digit 6 changes in the numbers represented
in Questions 12C and 12D.
TG • Grade 5 • Unit 8 • Lesson 3 • Answer Key 4
Answer Key • Lesson 3: Many Ways to Show Decimals
Student Activity Book
Name
Date
Decimal Grids: Hundredths
1. A. Shade twenty-three hundredths of the grid.
B. Write twenty-three hundredths as a
decimal fraction.
Decimal Grids: Hundredths (SAB pp. 299–300)
Questions 1–3
1. A.
Grace shows the decimal 0.23 on a number line. Since she knows that 0.23 is
between two tenths and three tenths she uses these decimals to label the ends of
her number line.
0.2
0.3
0.23
Grace used a dot to show the location of twenty-three hundredths.
47
100
2. A. Shade ⫺⫺ of the grid.
47 as a decimal fraction.
B. Write ⫺
⫺
100
Copyright © Kendall Hunt Publishing Company
B. 0.23
2. A.
Many Ways to Show Decimals
SAB • Grade 5 • Unit 8 • Lesson 3
299
Student Activity Book - Page 299
Name
B. 0.47
C.
Date
0.4
0.47
0.5
Copyright © Kendall Hunt Publishing Company
47 on the number line. First decide
C. Use Grace’s strategy to locate ⫺
⫺
100
between which tenths the decimal is located. Label the end points of the
number line with these tenths. Then place a dot on the number line to
show the location of the decimal.
D. 0.53
3. A.
D. Name the fraction of the grid that is not shaded. Write a decimal
fraction.
3. A. Shade sixty-eight hundredths of the grid.
B. Write sixty-eight hundredths as a
decimal fraction.
D. Locate sixty-eight hundredths on the number line.
Copyright © Kendall Hunt Publishing Company
C. Use expanded form to represent
sixty-eight hundredths.
E. Name the fraction of the grid that is not shaded. Write a decimal fraction
and a number sentence in expanded form.
B. 0.68
C. .6 +.08 = .68
D.
0.6
300
SAB • Grade 5 • Unit 8 • Lesson 3
Many Ways to Show Decimals
Student Activity Book - Page 300
5
TG • Grade 5 • Unit 8 • Lesson 3 • Answer Key
E. .3 +.02 = .32
0.68
0.7
Answer Key • Lesson 3: Many Ways to Show Decimals
Show Decimals (SAB pp. 301–304)
Questions 1–7
1.
.047
____________
decimal
Name
Date
Show Decimals
47—
——
1000
____________
fraction
Complete the missing information to show the decimal in each box in many
ways. The first one is done as an example. Use the Writing Numbers in Words
page in the Student Guide Reference section.
fourty-seven thousandths
_______________________________
words
Example
.47
____________
decimal
.04 + .007 = .047
_______________________________
expanded form
47
—
100
____________
fraction
forty-seven hundredths
_______________________________
words
.4 .07 .47
_______________________________
expanded form
0
1
.047
.4
1.
____________
decimal
Copyright © Kendall Hunt Publishing Company
.5
.47
——
—47
1000
____________
fraction
_______________________________
words
_______________________________
expanded form
.1
0
Many Ways to Show Decimals
SAB • Grade 5 • Unit 8 • Lesson 3
301
Student Activity Book - Page 301
2.
.65
____________
decimal
65
—
—
100
____________
fraction
Name
Date
2.
____________
decimal
sixty-five hundredths
_______________________________
words
_______________________________
words
.60 + .05 = .65
_______________________________
expanded form
_______________________________
expanded form
.65
1
1
0
3.
3.
.72
____________
decimal
____________
decimal
72
—
—
100
____________
fraction
_______________________________
words
sevety-two hundredths
_______________________________
words
_______________________________
expanded form
.70 + .02 = .72
_______________________________
expanded form
.7
.72
____________
fraction
.7
.72
.8
Copyright © Kendall Hunt Publishing Company
Copyright © Kendall Hunt Publishing Company
0
____________
fraction
.8
302
SAB • Grade 5 • Unit 8 • Lesson 3
Many Ways to Show Decimals
Student Activity Book - Page 302
TG • Grade 5 • Unit 8 • Lesson 3 • Answer Key 6
Answer Key • Lesson 3: Many Ways to Show Decimals
4.
Name
Date
.75
____________
decimal
75
—
—
100
____________
fraction
4.
.75
____________
decimal
____________
fraction
seventy-five hundredths
_______________________________
words
_______________________________
words
.70 + .05 = .75
_______________________________
expanded form
_______________________________
expanded form
.7
5.
18
———
5.
100
____________
fraction
____________
decimal
.18
____________
decimal
_______________________________
words
Copyright © Kendall Hunt Publishing Company
.75
.8
18
———
100
____________
fraction
eighteen hundredths
_______________________________
words
_______________________________
expanded form
.10 + .08 = .18
_______________________________
expanded form
0
Many Ways to Show Decimals
SAB • Grade 5 • Unit 8 • Lesson 3
.18
1
303
Student Activity Book - Page 303
Name
6.
Date
.094
____________
decimal
94—
——
1000
____________
fraction
6.
____________
fraction
ninety-four thousandths
_______________________________
words
_______________________________
words
.09 + .004 = .094
_______________________________
expanded form
_______________________________
expanded form
.094 .1
0
.1
0
7.
____________
fraction
Copyright © Kendall Hunt Publishing Company
.652
____________
decimal
_______________________________
words
_______________________________
expanded form
7.
.652
____________
decimal
hundred fifty-two thousandths
six
_______________________________
words
.600 + .05 + .002 = .652
_______________________________
expanded form
.6
304
SAB • Grade 5 • Unit 8 • Lesson 3
Many Ways to Show Decimals
Student Activity Book - Page 304
7
TG • Grade 5 • Unit 8 • Lesson 3 • Answer Key
652
—
—
1000
____________
fraction
.652
.7
Copyright © Kendall Hunt Publishing Company
____________
decimal
Answer Key • Lesson 3: Many Ways to Show Decimals
Represent Decimals (SAB pp. 305–308)
Homework
Questions 1–7
1.
.263
____________
decimal
Name
Date
Represent Decimals
263
———
1000
____________
fraction
Fill in the missing information. The first one is done as an example.
Example:
0.53
____________
decimal
two hunredths sixty-three thousands
______________________________________
words
fifty-three hundredths
_______________________________
words
.200 + .06 + .003 = .263
_______________________________
expanded form
.2
53
—
100
____________
fraction
.5 .03
_______________________________
expanded form
.3
.263
0.53
0.5
1.
263
———
1000
____________
fraction
____________
decimal
Copyright © Kendall Hunt Publishing Company
0.6
_______________________________
words
_______________________________
expanded form
.3
.2
Many Ways to Show Decimals
SAB • Grade 5 • Unit 8 • Lesson 3
305
Student Activity Book - Page 305
Name
2.
0.573
____________
decimal
Date
573
—
—
1000
____________
2.
fraction
0.573
____________
decimal
five hundred seventy-three thousandths
______________________________________
words
____________
fraction
_______________________________
words
.500 + .07 + .003 = .573
_______________________________
expanded form
_______________________________
expanded form
.5
.573
.6
3.
3.
.807
____________
decimal
____________
decimal
807
—
—
1000
____________
_______________________________
words
fraction
0.8 .007
_______________________________
expanded form
hundred seven thousandths
eight
_______________________________
words
0.8 .007
_______________________________
expanded form
0.8 .807
____________
fraction
Copyright © Kendall Hunt Publishing Company
Copyright © Kendall Hunt Publishing Company
.5
0.8
0.9
0.9
306
SAB • Grade 5 • Unit 8 • Lesson 3
Many Ways to Show Decimals
Student Activity Book - Page 306
TG • Grade 5 • Unit 8 • Lesson 3 • Answer Key 8
Answer Key • Lesson 3: Many Ways to Show Decimals
4.
Name
93
–––
.93
____________
decimal
Date
100
____________
fraction
4.
____________
decimal
ninety-three hundredths
_______________________________
words
____________
fraction
_______________________________
words
.9 + .03 = .93
_______________________________
expanded form
_______________________________
expanded form
.9
.9
5.
5.
____________
fraction
____________
decimal
.724
____________
decimal
Copyright © Kendall Hunt Publishing Company
seven hundred twenty-four thousandths
___________________________________
words
1.0
.93
1.0
724
——
—
1000
____________
fraction
seven hundred twenty-four thousandths
___________________________________
words
___________________________________
expanded form
+ .02 + .004 = .724
.700
___________________________________
expanded form
0.7
0.7
Many Ways to Show Decimals
SAB • Grade 5 • Unit 8 • Lesson 3
.8
.724
307
Student Activity Book - Page 307
6.
Name
.06
____________
decimal
Date
6.
six hundredths
_______________________________
words
____________
fraction
.0 + .06 = .06
_______________________________
expanded form
_______________________________
words
_______________________________
expanded form
0
.06
7.
7.
____________
fraction
Copyright © Kendall Hunt Publishing Company
.065
____________
decimal
_______________________________
words
_______________________________
expanded form
.065
____________
decimal
SAB • Grade 5 • Unit 8 • Lesson 3
Many Ways to Show Decimals
Student Activity Book - Page 308
9
TG • Grade 5 • Unit 8 • Lesson 3 • Answer Key
65
—
—
1000
____________
fraction
sixty-five thousandths
_______________________________
words
.06 + .005 = .065
_______________________________
expanded form
.06
308
.1
.065
.07
Copyright © Kendall Hunt Publishing Company
.06
____________
decimal
—6—
100
____________
fraction