13. The names of the first ten numbers and the names unit, hundred, thousand, million, etc., are simple words. By combining these names, other number names are formed. Thus, four hundred, three thousand, seven million, four hundred thousand. 14. The decimal system originated in India. But it came to us through the Arabs. Hence, it is called the Arabic system. 15. By means of the nine digit figures, the 0, and a dot (.), called the decimal point, any number can be expressed. 16. Illustrative Examples. (1) Express as one number 6 tenthousands, 4 thousands, 3 hundreds, 7 tens, 2 units. ILLUSTRATION ten-thousands → thousands chundreds tens decimal point 6 4,3 7 2 EXPLANATION. In writing numbers, to express units we write a figure in the first place at the left of the position of the decimal point, to express tens we write a figure in the second place at the left, to express hundreds we write a figure in the third place, to express thousands we write a figure in the fourth place, to express ten-thousands we write a figure in the fifth place, and so on. Hence, the above is written as one number thus, 64,372. 64,372 is read sixty-four thousand three hundred seventy-two. (2) Write four hundred and six units. EXPLANATION. We write thus, 406, putting a zero in the tens' place to show that there are no tens to be expressed. Whenever there is no number of a certain place to be expressed, we supply the place with a zero. 17. By the Arabic notation each figure always expresses the same number of units. 18. Written with other figures, each figure in any place expresses units of the place it occupies. This is called the local value of the figure. 19. Each figure in any place expresses ten times what it would represent if written in the next place to the right, and one tenth what it would represent if written in the next place to the left. 20. Illustrative Example. Write 6437 and 2 tenths; 643 and 72 hundredths; 64 and 372 thousandths. EXPLANATION. If we place a decimal point in 64,372 at the left of 2, thus, 6437.2, each figure expresses one tenth as much as before; the 2 (units) express 2 tenths, the 7 (tens) express 7 units, and so on. If we place the decimal point in 6437.2 at the left of 7, thus, 643.72, the 2 expresses 2 hundredths, the 7 expresses 7 tenths, and so on. 21. Whole numbers are called integral numbers or integers. Thus, 5, 29, 4329050 are integers. Parts of whole numbers are called fractions. We read 6437.2, six thousand four hundred thirty-seven and two tenths; 643.72, six hundred forty-three and seventytwo hundredths; 64.372, sixty-four and three hundred seventytwo thousandths. Taken in order, figures to the right of thousandths express ten-thousandths, hundred-thousandths, millionths, ten-millionths, and so on. 22. The following table shows how the groups and orders of units are written by the Arabic notation: The uppermost number above is read thus, 480 trillion, 297 billion, 34 million, 508 thousand, 672, and 8 thousand 345 tenthousandths. Oral Exercise 23. 1. Read the other numbers written beneath the table. 2. Read the number 345,345,345.345. In reading the above numbers, notice that each group takes its name from the right-hand place in the group. Notice, too, that no name is read for the ones' group. When whole numbers and fractions are written together, in reading the expression, we use and before the fractional part. 3. What name is given to the 2d group at the left of the decimal point? What name is given to the 3d group at the left? to the 4th? to the 5th? 4. What is the position of the thousands' group? the millions' group? the trillions' group? Oral Exercise 24. Beginning at the left, give the name of the place of each figure in the following: thus (1) 4 thousands, 8 hundreds, 7 tens, 5 units (ones). 9. What is the first place at the left of units called? What is the first place at the right of units called? 10. Give alternately the names of the places from the 1st to the 7th, at the right and left of units. 11. What is the name of the 3d place at the left of the decimal point? at the right? 12. What is the position with reference to the decimal point of the thousands' place? the millions'? the billions'? the thousandths'? the millionths'? 25. Illustrative Example. Read 1504670389. EXPLANATION. Beginning with units' group and counting the groups, we find 1 in the 4th, or billions', group. From left to right, the expression reads 1 billion, 504 million, 670 thousand, 389. Read: 1. 48790 9. 38904918 17. .862 25. 92.3046 2. 9078 10. 1760480 18. .704 26. 501.501 3. 84000 11. 300708 19. .067 27. 200.007 4. 40762 12. 447516300 20. .840 28. .207 5. 11094 13. 80040704 21. 981.2 29. .8483 6. 304091 14. 2321987650 22. 5.558 30. 8000.0483 7. 460203 15. 9876004381 23. .1476 31. .00116 16. 18073063918 24. 40.08 32. 100.00016 8. 510510 Written Exercise 26. Illustrative Example. Write in figures nineteen million one hundred thirty thousand three hundred sixteen and fourteen thousandths. EXPLANATION. Beginning with the highest, or millions', group, we write the groups in order from left to right, thus, 19,130,316.014. Write in figures and point off: 1. Six hundred seventy and sixty-seven thousandths. 2. Two thousand one hundred fourteen and thirteen hundredths. 3. Fourteen thousand five hundred and five tenths. 4. Five million thirty-six thousand six hundred ten. 5. One hundred sixty million one hundred thousand forty-one. 6. Two hundred seven and one hundred seventeen ten-thousandths. 7. Forty-three million seven hundred thousand two hundred sixty-seven. 8. Nine hundred one million two hundred eighteen thousand five hundred twenty-two. 9. Three and one thousand four hundred sixteen tenthousandths. 10. Sixteen and six thousand six hundred sixty-six tenthousandths. 11. Eighty-three and three hundred thirty-four thousandths. 12. Fifty-six thousand four hundred thirty-seven millionths. 13. Seven hundred and thirty-six thousandths. 14. Seven hundred thirty-six thousandths. 15. Four hundred and fourteen millionths. 16. Four hundred fourteen millionths. 17. Five hundred sixty-eight hundred-thousandths. |