Thus, 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.
As we continue from right to left, there are more periods. The five periods listed above are the most common, and in our study of introductory mathematics, they are sufficient.
The following diagram illustrates our positional number system to trillions. (There are, to be sure, other periods.)
In our positional number system, the value of a digit is determined by its position in the number.
Sample set b
Find the value of 6 in the number 7,261.
Since 6 is in the tens position of the units period, its value is 6 tens.
6 tens = 60
Find the value of 9 in the number 86,932,106,005.
Since 9 is in the hundreds position of the millions period, its value is 9 hundred millions.
9 hundred millions = 9 hundred million
Find the value of 2 in the number 102,001.
Since 2 is in the ones position of the thousands period, its value is 2 one thousands.
2 one thousands = 2 thousand
Practice set b
Find the value of 4 in the number 439,997,007,010.
four hundred billion
Whole numbers
Whole numbers
Numbers that are formed using only the digits0 1 2 3 4 5 6 7 8 9
are called whole numbers . They are
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, …
The three dots at the end mean "and so on in this same pattern."
Graphing whole numbers
Number line
Whole numbers may 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.
Origin
This point is called the origin . We then choose some convenient length, and moving to the right, mark off consecutive intervals (parts) along the line starting at 0. We label each new interval endpoint with the next whole number.
Graphing
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."Sample set c
Specify the whole numbers that are graphed on the following number line. The break in the number line indicates that we are aware of the whole numbers between 0 and 106, and 107 and 872, but we are not listing them due to space limitations.
The numbers that have been graphed are
0, 106, 873, 874
Practice set c
Specify the whole numbers that are graphed on the following number line.
4, 5, 6, 113, 978
A line is composed of an endless number of points. Notice that we have labeled only some of them. As we proceed, we will discover new types of numbers and determine their location on the number line.
Exercises
What is a numeral?
Does the word "eleven" qualify as a numeral?
Yes, since it is a symbol that represents a number.
How many different digits are there?
Our number system, the Hindu-Arabic number system, is a
positional; 10
Numbers composed of more than three digits are sometimes separated into groups of three by commas. These groups of three are called
In our number system, each period has three values assigned to it. These values are the same for each period. From right to left, what are they?
ones, tens, hundreds
Each period has its own particular name. From right to left, what are the names of the first four?
In the number 3,392, how many ones are there?
In the number 779,844,205, how many ten millions are there?
In the number 65,021, how many hundred thousands are there?
0
For following problems, give the value of the indicated digit in the given number.
9 in 29,827
Write a two-digit number that has an eight in the tens position.
Write a four-digit number that has a one in the thousands position and a zero in the ones position.
1,340 (answers may vary)
How many two-digit whole numbers are there?
How many four-digit whole numbers are there?
Is there a smallest whole number? If so, what is it?
yes; zero
Is there a largest whole number? If so, what is it?
The whole numbers can be visually displayed on a
Graph (visually display) the following whole numbers on the number line below: 0, 1, 31, 34.
Construct a number line in the space provided below and graph (visually display) the following whole numbers: 84, 85, 901, 1006, 1007.
Specify, if any, the whole numbers that are graphed on the following number line.
61, 99, 100, 102
Specify, if any, the whole numbers that are graphed on the following number line.