PRACTICAL ARITHMETIC NOTATION AND NUMERATION NOTE. NOTATION The definition of notation and other terms with which the pupil has become familiar while in the grades below, will be found on pages 337–350. Write in figures: 1. One hundred seventy-five million. 2. Three hundred twenty-four thousand. 3. Five hundred seventy-eight. 4. Eight hundred twenty-four million six hundred seventy-five thousand four hundred twenty-two. a. Find the sum of the above numbers. Write in figures, using the decimal point: 5. Two hundred seventy-five millionths. 6. Two hundred seventy-five hundred-thousandths. 7. Two hundred seventy-five ten-thousandths. 8. Two hundred seventy-five thousandths. b. Find the sum of the above numbers. Write in figures, using the decimal point: 9. One hundred forty-six and three tenths. 10. Two hundred fifty-four and two hundredths. 11. Six hundred ninety-six and five thousandths. c. Find the sum of the above numbers. Write in figures: 1. Four million forty thousand four. 2. Forty million four hundred thousand forty. 3. Four hundred million four thousand four hundred. a. Find the sum of the above numbers. Write in figures, using the decimal point: b. Find the sum of the above numbers. Write in figures, using the decimal point: 8. Four hundred seventy-eight tenths.† 9. Seven hundred forty-five hundredths. 10. Two thousand one hundred thirty-five thousandths. c. Find the sum of the above numbers. Write in figures, using the decimal point when necessary: 11. Two hundred fifty-four thousand one hundred sixty. 12. One hundred seventy-five and two hundred six thousandths. d. Find the sum of the above numbers. * In expressions like this, the word and may be thought of as standing for the decimal point in the figure notation. After writing the number, read it in the usual way forty-seven and eight tenths. Read each of the following in the usual way, using the word and only in place of the decimal point. 546.85 is five hundred forty-six and eighty-five hundredths. a. Copy the above numbers, arranging them with reference to convenience in adding, and find their sum. Observe that any mixed decimal may be read as though it were integral by giving the name of the units denoted by the righthand figure to the entire number; thus, 21.8 is 218 tenths; 5.36 is 536 hundredths; 24.305 is 24305 thousandths. Read each of the following as though it were integral, giving the name of the units denoted by the right-hand figure to the entire number: b. Copy the above numbers, and find their sum. Observe that any part of the consecutive figures of a number may be read by giving the name of the units denoted by the last figure of the part, to the entire part, thus: 24.65 may be thought of and read as 246 tenths and 5 hundredths; 14.275 as 142 tenths and 75 thousandths, or as 1427 hundredths and 5 thousandths. In a similar manner read each of the following: c. Copy the above numbers, and find their sum. Observe that in reading such numbers as the following it is only by the use or the omission of the word and that one can distinguish between the number (or numbers) on the left and the number in the same line on the right. a. Copy the above numbers, arranging them with` reference to convenience in adding, and find their sum. Read the following by telling the number of units in each order; thus, 346.25 is 3 hundreds, 4 tens, 6 primary units, 2 tenths, and 5 hundredths. 5. 467.34 8. 147.21 6. 24.176 9. 30.108 7. 3.2461 10. 2.3046 b. Copy the above numbers and find their sum. Observe that the units of any one order may be thought of as an equal number of tenths of one of the next higher order; thus, in the number 324.576, the 6 thousandths are 6 tenths of a hundredth; the 7 hundredths are 7 tenths of a tenth; the 5 tenths are 5 tenths of one primary unit; the 4 units are 4 tenths of a ten; the 2 hundreds are 2 tenths of a thousand. Again, the units of any one order may be thought of as ten times as many units of the next lower order; thus, in the number 253.475, the 2 hundreds are 20 tens; the 5 tens are 50 primary units; the 3 primary units are 30 tenths; the 7 hundredths are 70 thousandths. Tell the value of some of the units of the different orders in the following numbers in units of the next higher and the next lower orders: 11. 345.678 12. 453.876 13. 268.754 ADDITION NOTE. For definitions of terms see page 339. 1. In each of the above examples, tell which are the addends, and which is the sum. In written problems in addition the figures that stand for units of the same order are usually written in the same column. 2. In example b what figures represent units of the second decimal order? Of the third decimal order? 3. In example c what figures represent units of the first integral order? Of the second integral order? Only like numbers can be added. The denomination of the sum is the same as that of the addends. There are forty-five primary facts of addition. These are given in full on page 340. The nine primary facts often requiring special drill for their complete mastery are given below. |