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How to read Numbers.

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  1. 1. HOW TO READ AND WRITE WHOLE NUMBERS THE POWERS OF 10 In this Lesson, we will answer the following: 1.What are the ten digits? 2.Which numbers are the powers of 10? 3.What are the names of the classes? 4.How do we read a whole number, however large? Section 2: Place value. Positional numeration. To which place does each digit belong? What does it mean to write a number in expanded form? What is the relationship between the units of adjacent place value? How do we round off, or approximate, a whole number to a given place?
  2. 2. What are the ten digits? The ten symbols: 0 1 2 3 4 5 6 7 8 9 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 because it was the Arab mathematicians who introduced them into Europe from India, where their forms evolved. 364' is a , which is a symbol for a number. A number is the actual collection of .
  3. 3. The number we call One Thousand is a collection of ten One Hundreds. The powers of 10 Number Ten is a collection of ten Ones One Hundred is a collection of ten Tens. The number we call One Thousand a collection of ten One Hundreds.
  4. 4. The Powers of 10 Which numbers are the powers of 10? They are the numbers produced when, starting with One, we repeatedly collect them into groups of 10. 10 Ones. 10 Tens. 10 Hundreds. 10 Thousands. And so on. Here are their names and numerals. Class of One 1 Ones Ten 10 Hundred 100 Class of One thousand 1,000 Thousands Ten thousand 10,000 Hundred thousand 100,000 Class of One million 1,000,000 Millions Ten million 10,000,000 Hundred million 100,000,000 Class of One billion 1,000,000,000 Billions Ten billion 10,000,000,000 Hundred billion 100,000,000,000 Each power is composed of ten of the one above. (The metric system is the system of measurement based on the powers of 10; see ) Strictly, 1 is not a power of 10. The first power of 10 is 10 itself. Its numeral is a 1 followed by 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.
  5. 5. 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. Note that 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. In previous lesson we showed how to read and write any number from 1 to 999, which are the numbers in the class of Ones. Together with knowing the sequence of class names, that is all that is necessary to be able to name or read any whole number. 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." 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."
  6. 6. 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: 002 "Two" 020 "Twenty" 200 "Two hundred" 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. (For example, we should write $609.50 as "Six hundred nine dollars and fifty cents." Not "Six hundred and nine dollars.")
  7. 7. 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:
  8. 8. 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. a) Two hundred seventeen million b) Two hundred million seven teen Answers. a) 217,000,000 b) 200,000,017 Example 6. Distinguish the following: