24. Two hundred one thousand, one.

25. Seventy-two thousand, four.

NUMERATION

In reading a number we read the hundreds, tens, and units of its left-hand group, and then the name of that group; then we read the other groups in like manner proceeding towards the right. The names of the units' group and the name zero are omitted in reading. To illustrate :

454 tens, 5 ones; 45 is read "forty-five."

606 tens, 0 ones; 60 is read "sixty."

345 = 3 hundreds, 5 tens, 4 ones; 345 is read “three hundred fifty-four."

2093 2 thousands, 0 hundreds, 9 tens, 3 ones; 2093 is read "two thousand ninety three."

43796 is read "forty-three thousand seven hundred ninety-six."

3,405,072 is read three million, four hundred five thousand, seventy-two.

65,834,217 is read sixty-five million, eight hundred thirty-four thousand, two hundred seventeen.

28. What is the largest number expressed by two figures?

29. What is the smallest number expressed by two figures?

30. What is the largest number expressed by three figures?

31. What is the smallest number expressed by three figures?

32. Write the largest number expressed by the figures 0, 4, 5.

33. Write the smallest number expressed by the figures 0, 4, 5.

34. Write three numbers expressed by the figures 2, 3, 4. 35. Write four numbers expressed by the figures 7, 6, 8. Write three numbers expressed by the figures 9, 3, 8.

36. What is the largest number expressed by the figures 7, 3, 2, 8?

37. What is the smallest number expressed by the figures 2, 5, 3, 4?

NOTATION OF COMMON FRACTIONS

If the rectangle ABCD is divided into four equal parts, one of these parts is called one fourth of the rectangle; two of the parts are called two fourths of the rectangle; three of the parts are called three fourths of the rectangle; and four of the parts are called four fourths of the rectangle. In general, if any one thing is divided

into four equal parts, one of these parts is called a fourth; two of the parts are called two fourths; three

Simi

of the parts, three fourths, etc.
larly, if any thing is divided into five
equal parts, one of the parts is called

A

E

B

one fifth; two of the parts are called two fifths; three of the parts, three fifths, etc.

In the above rectangle, if the line EF is drawn so as to divide AB and DC each into two equal parts, the whole figure will be broken up into eight equal rectangles; one of these rectangles is one eighth of the whole; two of them are two eighths; three of them, three eighths, etc. Draw a larger rectangle like the one in the book. Letter it.

Divide AE and also EB each into three equal parts and draw through the points of division lines parallel to BC. What part of ABDC is one of the small rectangles? two of them? etc.

1 eighth is written }. 3 eighths is written . 5 eighths is written §.

2 eighths is written .

4 eighths is written. 6 eighths is written §, etc. How many thirds in 1 thing? How many fourths in 1 thing? How many sevenths in 1 thing? How many eighths in 1 thing? How many tenths in 1 thing?

Numbers indicated by such symbols as the above are called fractions.

Fractions represent one or more of the equal parts into which a number is divided.

In a fraction the number below the line is called the

denominator, meaning namer, because it names the parts into which the quantity is divided.

The number above the line is called the numerator, meaning numberer, because it tells the number of parts taken. Thus, signifies that the quantity is broken into 4 equal parts, and 3 of these parts are taken; 3 is the numerator, and 4 is the denominator.

The numerator and the denominator are called the terms of the fraction.

A proper fraction is one whose numerator is less than its denominator. Thus, is a proper fraction.

An improper fraction is one whose numerator equals, or is greater than, its denominator. Examples: 4, 7.

A mixed number is a number made up of a whole number and a fraction. Thus, 4 is a mixed number.

Read the following fractions and tell what kind of fraction each is:

3

f,

3, 4, §, 3, 1, 1, I, I, I, 4, 48, f, 8, 7, 8, 1o, §, 7, 8, 1, 4, §, 5, 7, 48, 8, §, 7, 8, 11, 15, 10, 16, 18, 18.

9

NOTATION OF DECIMAL FRACTIONS

The word decimal comes from the Latin, decem, meaning ten.

A fraction whose denominator is 10, 100, 1000, 10,000, etc., is called a decimal fraction, or simply a decimal; thus, 10, 180, 1000, are decimal fractions.

A more convenient form for writing decimal fractions is merely an extension of our method of writing whole numbers.

In writing a whole number we named the places toward the left, beginning at the units' place. If we put a dot at the right of the units' place and name the places toward the right, as shown in the table on the next page, we have

decimal fractions. Thus, may be written .9; is written .02, 100 is written .007.

The dot at the right of the units' place is called the decimal point.

Figures occupying places at the right of the decimal point represent the numerator of a decimal fraction whose denominator is indicated by the place occupied by the right-hand figure. That is, .9 stands for; .0023 stands

23

for 10000

Zeros are used to fill places between the decimal point and the first significant figure.

Zeros at the right of a decimal may be dropped, as they do not affect its value.

The following table shows the names of the places to the right of the decimal point; thus, 5 millionths is written .000005; 23 thousandths is written .023.

9 7 6.1

In writing a mixed number, the decimal point is placed after the whole number and then the decimal part is written; thus, twenty-five and thirty-three hundredths is written, 25.33.

The law of the decimal system of notation is: The value of a digit in any place is always ten times the value of the same digit written in the next place to the right.