<< Chapter < Page | Chapter >> Page > |
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 off consecutive and equal intervals (parts) along the line starting at 0. We label each new interval endpoint with the next whole number.
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.”
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.
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.
Because our number system is a positional number system, reading and writing whole numbers is quite simple.
To convert a number that is formed by digits into a verbal phrase, use the following method:
Here are a few examples for writing the numbers as words.
Write out 42958.
Solution: Forty-two thousand, nine hundred fifty-eight.
Write out 307991343.
Solution: Three hundred seven million, nine hundred ninety-one thousand, three hundred forty-three
Write out 36000000001.
Solution: Thirty-six trillion, one.
Write out each number in words.
Write out 12,341.
Twelve thousand, three hundred forty-one.
Write out 202,082,003.
Two hundred two million, eighty-two thousand, three.
Write out 1,000,010.
One million, ten.
For the following exercises, write the numbers for the following text.
Four hundred sixty thousand, five-hundred forty two.
460,542
Fourteen million, sixteen thousand, seven.
14,016,007
Three billion, eight-hundred three thousand.
3,000,803,000
Notification Switch
Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?