ADVANCED LESSONS

PART VIII

NOTATION AND NUMERATION

LESSON 1

The Higher Periods

Write eight; eight hundred; eight thousand; eight million. Which of these is the largest? Tell why.

Each of the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 has two values; one of these values is absolute and is expressed by the form of the figure; the other value is relative and depends upon the position that the figure occupies in a number. Thus, the figure "8" always has an absolute value of "eight," but in the number "894" the figure "8," besides having an absolute value of “eight,” also has a relative value of "eight hundred," since it occupies hundreds' place in this particular number.

In the same manner as 1,000 follows 999 and 1,000,000 follows 999,999, so we can have any number of places and periods, but more than five periods are seldom necessary to express a numerical value, as few things are so vast in their scope that more periods are necessary.

The first five periods-with three of which you are already entirely familiar and the names of the places they comprise are as follows:

The names of the next seven periods in their order are: quadrillions, quintillions, sextillions, septillions, octillions, nonillions, decillions.

Exercise 1-Oral.

1. In the number 764,384 what is the absolute value of each of the digits?

2. In the number 764,384 what is the relative value of each 4?

3. What determines the absolute value of a digit? 4. What determines the relative value of a digit? 5. What is the name of the first place of the 3d period

( 6,000,000)? What order is this when units' place is counted as the first? What places make up this full period?

6. What is the first place of the 4th period called? What places make up this period?

7. What is the first place of the 5th period called? What places make up this period?

8. What is the first place in any period called? The second place? The third place?

9. Name 5 periods; begin with units' period. 10. Beginning with units, name all the places to trillions' place.

Exercise 2-Oral.

Read the following statements smoothly:

1. Rays of heat from the sun travel 94,500,000 miles before they reach us in June; they travel 91,500,000 miles in January.

2. The distance across the earth's orbit is 186,000,000 miles the long way.

3. The area of the earth's surface is about 197,000,000 sq. mi.

4. The earth has about 1,700,000,000 people.

5. During the World War it was necessary for the United States to borrow money by issuing Liberty Bonds. The subscriptions for the Fourth Liberty Loan exceeded $6,000,000,000.00. 6. During the five years 1912-1916 inclusive, the average yearly production of the United States

was:

2,761,252,000 bu. corn.

1,296,406,000 bu. oats.

7. The lumber cut in the United States during the year 1917 was 35,821,239,000 ft.

8. To June 29, 1918, the Senate of the United States passed war bills aggregating $21,500,000,000.00 for conducting the World War.

9. The national wealth of the United States including all the real and personal property of every

description was estimated to be $187,739,000,000.00 in the year 1912.

10. Before the war the national wealth of France was approximately $63,000,000,000. and the national income about $7,500,000,000.

Exercise 3-Written.

Write:

1. Eight hundred forty-six billion, three hundred seventy-two million, one hundred forty-five thousand, nine hundred.

2. Four hundred sixteen billion, three hundred twenty-five thousand, four hundred sixty-two. 3. Eight hundred seventy-four trillion, three hundred twenty-one billion, four hundred sixty-two million, one hundred.

4. Six hundred five trillion, four hundred forty-five million, eight hundred thirty-one.

5. Thirty-eight trillion, seven hundred forty-six billion, one hundred forty-five.

6. Three hundred eighty-six trillion, four hundred ninety-eight million, two hundred twenty thousand, one.

7. Three hundred seven trillion, thirty-seven billion,

thirty million, seven hundred thousand, thirty. 8. Eight hundred twelve billion, eight hundred

million, twelve thousand, eight hundred twelve. 9. Sixty trillion, six hundred billion, six million, six hundred thousand, sixty-six.

10. Three hundred forty-five trillion, nine hundred eleven thousand.