9. Method of Reading Numbers.

(a.) To read a number expressed by figures, divide it into periods; and, beginning at the left, read the figures of each period as though they were followed by the name of the period.

ILLUSTRATION. -The number 34,068,250,006,789 is read as if written 34 trillion, 68 billion, 250 million, 6 thousand and 789.

(b.) Read each of the following numbers:

10. Method of Writing Numbers.

(a.) To express numbers by figures, write in each successive period the figures which show how many there are of the denomination of that period, taking care to fill each place, which is otherwise unoccupied, by a zero. The left-hand period may contain one, two, or three figures, but each of the others must contain three.

(b.) Write each of the following numbers in figures:

1. Nine thousand six hundred and fifty-eight

2. Twenty-nine thousand, six hundred and fifty-eight.

3. Eight hundred and twenty-nine thousand, six hundred and fifty-eight.

4. Three hundred and two thousand, three hundred and two. 5. Six thousand and sixty.

6. Ninety thousand, three hundred and eighty-seven.

7. Seventy thousand and seventy.

8. Four hundred and eighty-six thousand, five hundred and eighty-six.

9. Twenty-seven million, one hundred and eleven thousand, seven hundred and twelve.

10. Eight million, one hundred and seventy-six thousand, three hundred.

11. Five hundred and sixty million, three hundred and fourteen thousand, two hundred and forty-three.

12. Two million, two thousand, and seven.

13. Twenty million, twenty thousand, and seventy.

14. Two hundred million, two hundred thousand, two hundred. 15. Seventy-five million, twenty-five thousand, and twenty-four. 16. Two hundred and fifty million, two hundred and forty thousand, two hundred and forty.

17. Four million and five.

18. Forty-six million and forty-six.

19. Four hundred and sixty-nine million, four hundred and sixty-nine.

20. Eighty-seven billion, nine hundred and forty-three million, two hundred and seventy-eight thousand, four hundred and thirtytwo.

21. Six hundred and thirty billion, six hundred and thirty.

22. Ninety billion, ninety million, ninety thousand, and ninety. 23. Four hundred billion, four million, four hundred thousand and four.

24. Eight hundred and seventy-eight trillion, nine hundred and forty-three billion, seven hundred and thirty-six million, four hundred and nine thousand, eight hundred and thirteen.

25. Six hundred and thirteen quintillion, four hundred and sixty quadrillion, two hundred and three trillion, seven billion, sixtyeight thousand, and one.

11. Places at the Right of the Point.

(a.) The foregoing exercises and illustrations show that—

The figure occupying any place represents ten times the value it would represent if it stood one place farther to the right, and onetenth of the value it would represent if it stood one place farther to the left; one hundred times the value it would represent if it stood two places farther to the right, and one hundredth of the value it would represent if it stood two places farther to the left, etc. etc.

(b.) These principles extended would make the first figure at the right of the point represent tenths; the second, hundredths; the third, thousandths, etc. as illustrated below:

ANSWER.-3 tens, 7 units, 6 tenths, 8 hundredths, and 4 thousandths.

NOTE. The pupil should be very careful, in reading and speaking, to distinguish between tens and tenths, hundreds and hundredths, etc.

(c.) Numbers thus expressed by figures at the right of the point are called DECIMAL FRACTIONS.

They are so called because their denominator is always 10, 100, 1000, or some other power of ten -the word "decimal" being derived from the Latin word "decem," which means ten. When the denominator is written beneath the numerator, they have the form of VULGAR FRACTIONS.

12. Method of Reading Decimal Fractions.

(a.) Numbers containing decimal fractions may be read by first reading the figures at the left of the point as though they stood alone, and then reading the figures at the right of the point as though the name of the place occupied by the right-hand figure were written after them.

37 and 28 hundredths; .0067846 == 6000 and 6 thousandths.

ILLUSTRATIONS.- 37.28 millionths; 6 00.006

= 67846 ten

(c.) Numbers containing decimal fractions may also be read as if the point were omitted, and the name of the place occupied by the right-hand figure written after them.

ILLUSTRATIONS. -37.28

sandths; 6000.006 6000006 thousandths.

(d.) Read the numbers under b, by the last method.

NOTE. By this method they are read as IMPROPER FRACTIONS (see 76).

13. Method of Writing Decimal Fractions.

(a.) To represent decimal fractions by figures, write them as if they were whole numbers, and then mark the decimal point so as to bring the right-hand figure in the place bearing the name of the denominator of the given fraction.

(b.) There will always be as many places at the right of the point as there would be zeroes used in writing the denominator of the given fraction. When there are not figures enough for this in the numerator, zeroes must be prefixed to supply the deficiency.

ILLUSTRATIONS.-To write 479 hundredths, write 479 and place the point so that the 9 shall come in the hundredths' place; thus, 4.79. To write 6 hundred, and 47 millionths, write 600 and the point, and then write the 47 so that the 7 shall come in the millionths' place, which will require 4 zeroes between the point and the 47; thus, 600.000047.

(c.) Write each of the following numbers:

1. Six thousandths.

2. Forty-five hundredths.

3. Eight, and nine-tenths.

4. Eighty-nine tenths.

5. Eighty-nine hundredths.

6. Six, and five hundredths.

7. Twenty-nine, and four hundred and thirty-six thousandths. 8. Sixty-five ten-thousandths.

9. Eight hundred and thirteen tenths.

10. Eight hundred and thirteen hundredths.

11. Eight hundred and thirteen thousandths.

12. Sixty-one, and forty-two thousandths.

18. Five hundred and twenty-seven thousands, and five hundred and twenty-seven thousandths.

14. Nine hundred and fourteen million, two hundred and thirteen thousand, seven hundred and eight, and six hundred and eleven thousand, two hundred and sixty-eight millionths.

15. Seventy-one billionths.

16. Six thousand, and five tenths.

17. One hundred and forty-two thousand, four hundred and forty-eight ten-thousandths.

18. Seventy million, and nine millionths.

19. Eighty-nine million, eighty-nine thousand and eighty-nine, and eighty-nine million, eighty-nine thousand and eighty-nine billionths.

20. Three million, and three-hundred-thousandths.