1.1 Introduction to Whole Numbers
Finish filling out the check below. The amount of the check is given in words; write this amount, in numbers,
in the indicated space. For this exercise, do not worry about cents.
1629.00
Assess your readiness to complete this activity. Rate how well you understand:
Not
ready
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ready
Bring
it on!
• the terminology and notation used when reading and writing whole numbers
• the identification of place values
• the value of a digit with respect to its particular position in a number
• the meaning of zero as a placeholder
• the use of place value group words in reading and writing whole numbers
• the use of commas in writing numbers
Translating a number between words and standard notation
• use of correct place values and place value groups
• correct placement of commas
• correct spelling and use of hyphens
Chapter 1 — Whole Numbers
Technique
Working from left to right, say or write out the word name for the number in each place value
group (indicated by comma breaks) followed by the group name. Use commas in the written
form.
Note that starting from the ones place at the far right, place values are divided by commas into three-digit
groupings — ones, hundreds, thousands, etc. Some textbooks use the term period to refer to these while others
refer to them as place value groups. This book will use the latter phrase.
Translate each of the following numbers to its word form.
millions
thousands
7
7,243,603
A
►
2
seven
ones
4
3
6
two hundred forty-three
0
3
six hundred three
Answer: seven million, two hundred forty-three thousand,
six hundred three
billions
B
28,064,852,019
►
millions
2
8
twenty-eight
0
6
sixty-four
thousands
4
8
5
ones
2
eight hundred fifty-two
0
1
9
nineteen
Answer: twenty-eight billion, sixty-four million,
eight hundred fifty-two thousand, nineteen
550,009
C
►
Special
Case:
Answer: five hundred fifty thousand, nine
Three Placeholder Zeros
in a Place Value Group
4,000,975
D
►
When all three places in a place value group are
zeros, that group is not named in the word form.
The thousands place value group consists of three zero
placeholders, so “thousands” is not in the word form.
Answer: four million, nine hundred seventy-five
Activity 1.1 — Introduction to Whole Numbers
Technique
Working from left to right, substitute digits that correspond to the number stated for each
place value group and use commas in place of group names.
Special
Case:
A particular place value group is not in the
word form (see below, Models C & D)
Write each of the following numbers in standard form.
A
►
fifty-three thousand, four hundred seventy two
53
thousands
ones
5
472
3
4
7
2
Answer: 53,472
B
►
seventy-eight million, three hundred fifty-five thousand, four hundred sixty-two
78
462
355
millions
7
thousands
8
3
5
ones
5
4
6
2
Answer: 78,355,462
Special A Particular Place Value Group
Case: is Not in the Word Form
►
C
two million, one hundred twenty-eight
Use three placeholder zeros to represent a
place value group missing from the word form.
The thousands place value group is not
in the word form. Use three zeros as
placeholders for the thousands group.
Answer: 2,000,128
D
►
four hundred thousand
Use three zeros as placeholders for the ones group.
Answer: 400,000
Chapter 1 — Whole Numbers
Make Your Own Model
Either individually or as a team exercise, create a model demonstrating
how to solve the most difficult problem you can think of.
Answers will vary.
Problem: _________________________________________________________________________ 1. How do you determine a digit’s value in a number? Give an example.
Place value represents a specific position in a number. Each place value produces a contribution to the total number
by multiplying the digit occupying the place value position by the value of the place value.
All place values to the right of the first digit must be represented by a digit 0 – 9.
A zero place value contributes zero contribution to total number value.
2. When do you use the placeholder digit zero (0) in the standard form of a number? Give an example.
Zero is used as a placeholder when the number has none of a specific place value. In the number 702, there are 7
hundreds and 2 ones, but zero tens. This only holds when there is some larger place values.
3. When you translate a number into words, what do you do with place value groups that contain all zeros?
Give an example.
When all three places in a period are zeros, that period is not named in word form.
Example: 3,000,402 is read three million, four hundred two
Activity 1.1 — Introduction to Whole Numbers
4. What is the relationship between place value groups and commas when writing numbers in either words
or digits?
Commas are used to separate place value groups when writing numbers. Commas follow the place value group
name in words and are inserted before every third digit (place value group) beginning from right to left.
5. How is a place value chart used to translate numbers between words and digits?
To translate from digits to words, use the place value chart to identify each place value name for the digits of the
number. Match each digit with a place value column, then starting from left to right, say the set of digits with its
place value names and insert the place value group name as appropriate after each place value group. To translate
from words to digits, use the place value chart to identify each place value name describe to identify the digits of
the number.
6. How can you ensure that a translation of a whole number into a new representation is accurate?
The best way to validate that you translated correctly is to convert back to the original form while not looking at the
original presentation, then make sure that each place value position matches up to the original number.
7. When should you use numbers written in words rather than in digits?
While writing in most forms, it is the custom to write numbers less than ten in words. Words are needed in formal
documents to validate standard form, such as checks, contracts, and official newspaper postings. Words are also
needed in formal social documents like wedding announcements.
8. What aspect of the model you created is the most difficult to explain to someone else? Explain why.
Answers will vary.
Chapter 1 — Whole Numbers
1. Identify the place name as requested for the number 4,350,927.
a) The 2 is in the __tens_________________________________________ place.
b) The 4 is in the __millions_____________________________________ place.
c) The 3 is in the __hundred thousands_______________________ place.
d) The 0 is in the __thousands__________________________________ place.
2. Write the following numbers in standard notation.
3,681
a) three thousand, six hundred eighty-one_ ________________________________________
654,023
b) six hundred fifty-four thousand, twenty-three ____________________________________
5,028,404
c) five million, twenty-eight thousand, four hundred four_____________________________
7,000,650
d) seven million, six hundred fifty_ ______________________________________________
3. Write in word form.
two thousand, seven hudred forty-five
a) 2,745 __________________________________________________________________________
three hundred seventy-eight thousand, two hundred thirteen
b) 378,213__________________________________________________________________________
one million, three thousand, thirty
c) 1,003,030 ________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
_ _______________________________________________________________________
nine billion, four hundred twenty-two thousand
d) 9,000,422,000 ____________________________________________________________________
_ ____________________________________________________________________
Activity 1.1 — Introduction to Whole Numbers
1. Write in standard notation:
a) eighteen thousand, five hundred forty-two
18,542
b) seven million, one hundred two thousand, six hundred three
c) thiry-nine million, seven hundred sixty
7,102,603
39,000,760
d) one billion, two hundred million, three hundred forty-five thousand, one hundred
1,200,345,100
2. Write in words:
a) 498,555
b) 3,002,080
c) 11,000,346
four hundred ninety-eight thousand, five hundred fifty-five
three million, two thousand, eighty
eleven million, three hundred forty-six
d) 5,018,234,010
five billion, eighteen million, two hundred thirty-four thousand, ten
Identify and correct the errors in the following translations. The first one has been done for you.
Worked Solution
What is Wrong Here?
1) Translate “thirty-two
thousand, four hundred
fifty-six” to standard form
320,456
2) Translate “three million,
three hundred” to standard
form.
3,300,000
Identify the Errors
Correct Process
Should be 32 (two digits) in
the thousands rather than
320.
Answer:
32,456
Wrong place value for the second
three—presently represents
three hundred thousand rather
than three hundred.
3,000,300
Chapter 1 — Whole Numbers
Worked Solution
What is Wrong Here?
3) Translate 5703 to word
form.
fifty-seven hundred
and three
4) Translate 12,000,500 to
word form.
twelve thousand five
hundred
Identify the Errors
Correct Process
Did not use a comma to separate
periods. Five thousand, seven
hundred rather than fifty-seven
hundred. Also, use of the word
“and” not needed.
five thousand,
seven hundred
three
Wrong period. It is twelve million
rather than twelve thousand.
twelve million five
hundred