10. Since in a number like 1111.111, each 1 stands for 10 times as much as the next 1 toward the right, the first 1 following the decimal point stands for 1 of the 10 equal parts of a unit, called one tenth; the second for 1 of the 10 equal parts of one tenth, or 1 of the 100 equal parts of a unit, called one hundredth; the third for 1 of the 1000 equal parts of a unit, called one thousandth; etc.

What does each 3 in 33.333 represent? each 5 in 555.55? each 8 in 8888.888?

11. All figures on the left of the decimal point represent whole units, called integers.

All figures on the right of the decimal point represent parts of units, called decimals.

12. Figures in units' place express units of the first order; in tens' place, units of the second order; in hundreds' place, units of the third order; etc.

The decimal orders are numbered first, second, third, etc., from the decimal point toward the right.

13. The largest number that can be represented by three figures is 999; the smallest number that requires four figures to represent it is 1000.

Thousands are named in the same way as units; thus, 1 thousand, 2 thousand, 3 thousand, etc., up to 999 thousand; 1000 thousand is called one million (1,000,000).

Millions are named in the same way, 1000 million being called one billion (1,000,000,000); 1000 billion, one trillion (1,000,000,000,000); etc.

14. For convenience in writing and reading large numbers, the figures are separated by commas into groups of three figures each, called periods.

The highest or left-hand period may contain less than three figures.

15. The first period of integers, counting from the right, is used to denote any number from 1 to 999 units; the second, any number from 1 to 999 thousand; the third, any number from 1 to 999 million; etc.

16. The general arrangement of the orders of units and their separation into periods is illustrated by the following table:

TRILLIONS' BILLIONS' MILLIONS' THOUSANDS' UNITS'
PERIOD

PERIOD

PERIOD

PERIOD

PERIOD

The first number in the table is read, "37 trillion, 240 billion,

80 million, 438, and 75 thousandths."

Read the other numbers in the table.

17. Observe that

1. Each period beginning at the left is read as if it stood alone, the name of units' period, only, being omitted.

2. The figure 0 or a period of O's is not read.

3. The word "and" is not used, except between an integer and a decimal.

4. The decimal point precedes tenths' figure in all decimals. A decimal point may be assumed to follow the units' figure of all integers. 18. Other orders of decimals to the right of those in the table are ten-thousandths, hundred-thousandths, millionths, etc.

19. A number that is expressed by an integer and a decimal is called a mixed number or a mixed decimal.

20. Following is the fundamental principle of any decimal system:

Ten units of any order, integral or decimal, make one unit of the next higher order.

WRITTEN EXERCISES

22. Express by figures:

1. Twelve thousand, two hundred sixty.
2. Six hundred thousand, seven hundred one.
3. Nineteen thousand, eight hundred forty-two.
4. Seven hundred one thousand, ninety-eight.
5. Nine hundred ninety-nine thousand, seven.
6. Three million, three hundred thousand.
7. Sixty million, sixty thousand, forty-five.
8. Forty-six million, eight hundred sixty-two.
9. Thirteen million, fifty-five.

10. Two hundred seven million, five hundred seventy-one thousand, three hundred eight.

11. Five hundred two million, seven hundred six thousand, nine hundred twenty-three.

12. One hundred one million, three hundred four thousand, six hundred eighty-nine.

13. Four hundred two, and sixty-eight thousandths.

14. Ninety-six, and ninety-one ten-thousandths.

15. Two hundred eighty, and seventy-one millionths.

16. One million, one thousand, one, and one thousandth.

17. Six billion, four hundred seventy-one million, eight hundred thirty-six thousand.

18. Seventy-five billion, forty million, nine hundred eightyone thousand, three hundred four.

19. Two million, and seven tenths.

20. Seventy-two thousand, and sixteen thousandths. 21. Four hundred, and one hundred six millionths. 22. Two, and one thousand ninety-six ten-millionths.

EXERCISES

23. The dials of a gas meter, and of other kinds of meters, give readings in the decimal scale.

Each division on dial No. 1 represents 100 cubic feet of gas, and each complete revolution of the hand records the passage of "1 thousand" cubic feet of gas through the meter, as indicated over the top of the dial. With each complete revolution of the hand of No. 1, the hand of No. 2 moves from one division to the next, and 10 revolutions of the hand of any dial produce 1 revolution of the hand of the dial next on the left.

Each division on the small unit dial, used for testing, represents 1 cubic foot.

1. How much gas passes through the meter while the hand of No. 1 moves from 0 to 1? from 1 to 2?

2. How much gas is No. 1 recording?

3. How much gas passes through the meter while the hand of No. 2 moves from 0 to 1? from 0 to 2?

4. How much gas are No. 2 and No. 1 together recording? 5. How many complete revolutions has the hand of No. 2 made while the hand of No. 3 has been moving from 0 to its present position? Read No. 3, No. 2, and No. 1 together.

6. Read all the dials. How much gas is the meter recording now? What is the greatest amount of gas it will record?