The expression in the diagram is read as follows: Six trillion, three hundred and seventy-four billion, nine hundred and sixtyfive million, seventy-two thousand, one hundred and thirty-eight. This is the French method of naming numbers, and is the one universally adopted in the United States. A different plan prevails in England. There, a comma is usually written after every third figure of a long number, but each three figures constitute a half-group rather than a whole one, and the method of reading will be more clearly represented if we omit every other comma, and make the groups consist of six figures each. Thus, 6,374965,072138 Six billion, three hundred and seventy-four thousand nine hundred and sixty-five million, seventy-two thousand one hundred and thirty-eight. In the French method a billion is a thousand millions; a trillion, a thousand billions. In the English, a billion is a million millions; a trillion, a million billions. As numbers beyond millions are not often used, practically there is very little difference between the two methods. In the United States, although the French method is as a whole universally followed, numbers running over into the billions are quite commonly read as in England. Thus, Seventeen hundred million for 1,700,000,000. The English method is the more logical, billion, trillion, etc., being, as the names (bi-million, tri-million, etc.) signify, the second, third, etc., powers of a million. CLX represents one hundred and sixty. IV represents four, the greater value V being diminished by the lesser value I, which precedes it. IIII represents four. Except on the dials of clocks and watches, IV is used rather than IIII. IX represents nine. VIIII represents nine. IX is used rather than VIIII. XL represents forty. XC represents ninety. CX represents one hundred and ten. CCCC represents four hundred. CD represents four hundred. CM represents nine hundred. M represents one million. X10 =14 (10 and 4) XIX = 19 (10 and 9) XLV= 45 (40 and 5) XCIX = 99 (90 and 9) MDCCXLII represents seventeen hundred and forty-two thou sand. The general use of the vinculum (-) is to indicate that. the quantities over which it is placed are to be taken together as one quantity. The parenthesis () and brackets [ ] are used in a similar manner. Used over Romans, the vinculum means that the whole quantity stands for thousands. This use of the vinculum is sometimes found in old books and writings, but there is no longer any occasion for its use in the expression of numbers. The Roman numerals are used upon dials of clocks and watches, and also to mark chapters, sections, etc. They are not used for computation. To read a long number, we first point off mentally into groups of three figures each, naming each group as we go along. Thus, in the second number below, 34 are units; 000, thousands; 100, millions; 857, billions. The entire number is read as follows: Eight hundred and fifty-seven billion, one hundred million, and thirty-four. 7. Six hundred and seventy-three thousand, five hundred and twenty-one. 8. Seventy-five million, two hundred and eight thousand, and forty. 9. Seventy-six trillion, four thousand, and twenty-eight. 10. Eight hundred and seventy million, sixty-five thousand, and four hundred. 11. Five hundred and seventy billion, three hundred and forty-six million, two hundred and eighty-four thousand, and seven. 12. Express in Romans, the numbers from one to one hundred. ADDITION. If we start with 3, and count two numbers further, we get 5. We can do this by one step, - 3 and 2 are 5. When we say 3 and 2 are 5, we mean the second number greater than 3 is 5. If we count eight numbers beyond 5, we get 13. 5 and 8 are 13. 3 and 2 and 8 are 13. The process is called Addition. The sign of addition is an upright cross. 3+2 5. Three plus two equals five. 5 is called the sum of 3 and 2. 867 386 Sum 1253 6 units and 7 units are 13 units 1 ten and 3 units. 1 ten and 8 tens and 6 tens are 15 tens 1 hundred and 5 tens. 1 hundred and 3 hundreds and 8 hundreds are 12 hundreds. To test the result, begin at the top and add down. 6, 13, 21 8, 11, 16 3, 12, 15, 19 1961 SUBTRACTION. Begin at 8 and count five numbers backward; thus, 7, 6, 5, 4, 3. Or do it by one step: 8, 3. When we say 8 less 5 is 3, we mean the fifth number smaller than 8 is 3. The process is called Subtraction. The sign of subtraction is a short horizontal line. = 8-5 3. Eight minus five equals three. 8 is called the minuend; 5, the subtrahend; 3, the difference, or remainder. Minuend 6724 2 from 4 = 2. 4 from 2 is impossible in Arithmetic, so we take 1 from the 7 hundreds of the minuend and reduce it to 10 tens, which 8. 1 from 6 added to the 2 tens make 12 tens. 4 from (7 less the 1 already taken and used) = 5. Minuend 6003 Test. 2 and 2 are 4. 8 and 4 are 12. 1 and 5 and 1 are 7. 3 and 3 are 6. 12 = 3 from 6 = 3. Here we cannot take 7 from 3, and there are no tens in the minuend to go to, so we must go further. Neither are there any hundreds; so we must go further still, and take one of the 6 thousands, calling it 10 hundreds. Leaving 9 of the |