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Place Value and Names for Numbers
ADA
∗
Ann Simao
Based on Place Value and Names for Numbers† by
Rob Knight
Community College Online Textbook Project
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 3.0‡
Abstract
This module presents a denition of whole numbers and then talks about how numbers are named
in English. It presents the idea of periods, such as units, thousands, millions, and so on. It has several
exercises for writing out numbers into words.
1 Numbers and Numerals
Numbers that are formed using only the following digits are called
whole numbers:
0 1 2 3 4 5 6 7 8 9
The whole numbers in order are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
...
The three dots at the end mean and so on in the same pattern.
The whole numbers can be visualized by constructing a number line. To construct a number line, we
simply draw a straight line and choose any point on the line and label it 0. This point is called the origin.
We then choose some convenient length, and moving to the right, mark o consecutive and equal intervals
(parts) along the line starting at 0. We label each new interval endpoint with the next whole number.
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‡ http://creativecommons.org/licenses/by/3.0/
∗
†
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Figure 1
We can visually display a whole number by drawing a closed circle at the point labeled with that whole
number. Another phrase for visually displaying a whole number is graphing the whole number. The word
graph means to visually display.
2 The Names for Whole Numbers
The Hindu-Arabic numerals 0 1 2 3 4 5 6 7 8 9 are called digits. We can form any number in the number
system by selecting one or more digits and placing them in certain positions. Each position has a particular
value. The Hindu mathematician who devised the system in about 500 A.D. stated that from place to place
each is ten times the preceding. It is for this reason that our number system is called a positional number
system with base ten.
When numbers are composed of more than three digits, commas are sometimes used to separate the
digits into groups of three (such as 1,465,345). These groups of three are called periods, and they greatly
simplify reading numbers.
In the Hindu-Arabic numeration system, a period has a value assigned to each of its three positions, and
the values are the same for each period. The position values are from right to left ones, tens, hundreds.
Each period contains a position for the values of one, ten, and hundred. Notice that, in looking from
right to left, the value of each position is ten times the preceding. Each period has a particular name.
Figure 2
As we continue from right to left, there are more periods. The ve periods listed above are the most
common, and in our study of introductory mathematics, they are sucient.
The following diagram illustrates our positional number system to trillions. (There are, to be sure, other
periods.)
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Figure 3
In our positional number system, the
value of a digit is determined by its position in the number.
Because our number system is a positional number system, reading and writing whole numbers is quite
simple.
2.1 Reading Whole Numbers
To convert a number that is formed by digits into a verbal phrase, use the following method:
1. Beginning at the right and working right to left, separate the number into distinct periods by inserting
commas every three digits (e.g. 123456 becomes 123,456).
2. Beginning at the left, read each period individually, saying the period name.
Here are a few examples for writing the numbers as words.
2.1.1 Example 1
Write out 42958.
1. Beginning at the right, we can separate this number into distinct periods by inserting a comma between
the 2 and 9, which is 42,958.
2. Beginning at the left, we read each period individually:
•
•
Thousands period: __ 4 2
Units period: 9 5 8
→
→
Forty-two thousand,
nine hundred fty-eight.
Solution: Forty-two thousand, nine hundred fty-eight.
2.1.2 Example 2
Write out 307991343.
1. Beginning at the right, separate this number into distinct periods by placing commas between the 1
and 3, and the 7 and 9, resulting in 307,991,343.
2. Beginning at the left, read each period individually.
•
•
•
Millions period: 3 0 7
→
Thousands period: 9 9 1
Units period: 3 4 3
→
Three hundred seven million,
→
nine hundred ninety-one thousand,
three hundred forty-three.
Solution: Three hundred seven million, nine hundred ninety-one thousand, three hundred
forty-three
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2.1.3 Example 3
Write out 36000000001.
1. Beginning at the right, separate this number into distinct periods by placing commas, resulting in
36,000,000,001.
2. Beginning at the left, read each period individually.
•
•
•
•
•
→ Thirty-six trillion,
→ zero billion,
Millions period: 0 0 0 → zero million,
Thousands period: 0 0 0 → zero thousand,
Units period: 0 0 1 → one.
Trillions period: __ 3 6
Billions period: 0 0 0
Solution: Thirty-six trillion, one.
2.2 Exercises
Write out each number in words.
Exercise 1
(Solution on p. 5.)
Write out 12,341.
Exercise 2
(Solution on p. 5.)
Write out 202,082,003.
Exercise 3
(Solution on p. 5.)
Write out 1,000,010.
For the following exercises, write the numbers for the following text.
Exercise 4
(Solution on p. 5.)
Four hundred sixty thousand, ve-hundred forty two.
Exercise 5
(Solution on p. 5.)
Fourteen million, sixteen thousand, seven.
Exercise 6
Three billion, eight-hundred three thousand.
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(Solution on p. 5.)
OpenStax-CNX module: m47984
Solutions to Exercises in this Module
Solution to Exercise (p. 4)
Twelve thousand, three hundred forty-one.
Solution to Exercise (p. 4)
Two hundred two million, eighty-two thousand, three.
Solution to Exercise (p. 4)
One million, ten.
Solution to Exercise (p. 4)
460,542
Solution to Exercise (p. 4)
14,016,007
Solution to Exercise (p. 4)
3,000,803,000
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