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Lesson 1 READING AND WRITING
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Examples. 105 is a three-digit number. The digits are 1, 0, and 5. 28 ends in the digit 8. $364 has the same digits as $3.64. Those ten marks are also known as the Arabic numerals, because it was the Arab mathematicians who introduced them into Europe, where their forms evolved. A numeral, such as 364, is a symbol for a number. A number (at any rate, what we call a natural number) is the actual collection of units: /////. 'V' is the Roman numeral for five. '5' is the Arabic numeral. It is conventional however to call the symbols 1, 2, 3, 4, and so on, "numbers;" which they are not. |
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10 × 1 = 10 10 × 10 = 100 10 × 100 = 1000 And so on. The Powers of 10
Strictly, 1 is not a power of 10. The first power of 10 is 10 itself. It has one 0. The second power of 10 is 100; it has two 0's. The third power has three 0's. And so on. Notice how the names fall into groups of three: One thousand, Ten thousand, Hundred thousand. One million, Ten million, Hundred million. Each group of three -- Ones, Tens, Hundreds -- is called a class. |
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Each class is 1000 times the previous class; the Thousands are 1000 times the Ones; the Millions are 1000 times the Thousands; and so on. Starting with Billions (bi for two), each class has a Latin prefix. To read a number more easily, we separate each class -- each group of three digits -- by commas. We assume that the student can read any number from 1 to 999, and so we can now answer the following: |
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Example 1. Read this number: 256,312,785,649,408,163 Answer. Starting from the left, 256, read each three-digit group. Then say the name of the class. 
Say: "256 Quadrillion, 312 Trillion, 785 Billion, 649 Million, 408 Thousand, 163." Do not say the class name "Ones." The class of Ones, on the right, are the numbers 1 through 999. Together with the class names, they are the only numbers we need to know how to read. Example 2. To distinguish the classes, place commas in this number: 8792456 Answer. Starting from the right, place commas every three digits: 8,792,456 Read the number: "8 million, 792 thousand, 456." Example 3. Read this number: 7,000,020,002 Answer. "Seven billion , twenty thousand, two." When a class is absent, we do not say its name; we do not say, "Seven billion, no million, ..." Also, every class has three digits and so we must distinguish the following:
As for "and," in speech it is common to say "Six hundred and nine," but in writing we should reserve "and" for the decimal point, as we will see in the next Lesson. (For example, we should write $609.50 as "Six hundred nine dollars and fifty cents." Not "Six hundred and nine dollars.") Example 4. Write in numerals: Four hundred eight million, twenty-nine thousand, three hundred fifty-six. Answer. Pick out the classes: "million", "thousand". Each class (except perhaps the first class on the left) has exactly three digits: 
Example 5. Write in numerals: Five billion, sixteen thousand, nine. Answer. After the billions, we expect the millions, but it is absent. Therefore write 5,000,016,009 Again, we must write "sixteen thousand" as 016; and "nine" as 009; because each class must have three digits. The exception is the class on the extreme left. We may write "Five" as 5 rather than 005. When writing a four-digit number, such as four thousand five hundred, it is permissible to omit the comma and write 4500. In fact, we often read that as "Forty-five hundred." But when a number has more than four digits, then for the sake of clarity we should always place the commas. Example 6. Distinguish the following:
At this point, please "turn" the page and do some Problems. or Continue on to Section 2: Place value Introduction | Home | Table of Contents Please make a donation to keep TheMathPage online. Copyright © 2001-2008 Lawrence Spector Questions or comments? E-mail: themathpage@nyc.rr.com |
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