GRAMMAR SCHOOL ARITHMETIC ARABIC NOTATION AND NUMERATION 1. That which tells how many is number; e.g. three, seven, five, two and one half. 2. One is a unit; e.g. one, one (dollar), one (book). 3. A number that is applied to some particular thing or things is called a concrete number; e.g. five (books), seven (dollars), ten (months). 4. A number that is not applied to any particular thing or things is called an abstract number; e.g. five, seven, eleven. See Primary Arithmetic, pages 139 and 140. To the Teacher. 5. A number that is composed entirely of whole units is an integer; e.g. six, eight, thirteen. 6. One or more of the equal parts of a unit is a fraction; e.g. 1. §, 200. 25 7. The number above the line in a fraction is the numerator; the number below the line in a fraction is the denominator; e g. in the fractions, 3, and 6, the numerators are 2, 7, and 25. The denominators are 3, 8, and 100. 8. The product of equal factors is a power. (See § 47); e.g. 4 is a power of 2 8 is a power of 2 10 x 10 81 is a power of 3 because 3 × 3 × 3 × 3 100 is a power of 10 because 3 Name three other powers of 10. 9. A fraction whose denominator is 10 or a power of 10 is a decimal fraction; e.g. 10, 100, 14880, .7, .25, .0438. 25 10. Expressing numbers by means of figures or letters is notation; e.g. 32, XXXII. 11. Expressing numbers by means of figures is Arabic notation; e.g. 349, 6872.351. 1, 2, 3, 4, 5, 6, 7, 8, and 9 are called significant figures because they have values. The figure 0, called a cipher, naught, or zero, expresses no value. It is used to give the significant figures their proper places in expressing numbers. 12. The value of each significant figure depends upon the place which it occupies when used with other figures in expressing a number. The value of a figure in any place is ten times as great as it would be if it occupied the next place to the right, and one tenth as great as it would be if it occupied the next place to the left. Since the value of a figure is increased tenfold as it is moved one place from right to left, and divided by ten as it is moved one place from left to right, Arabic notation is said to be based on a scale of ten; or, the scale of Arabic notation is a decimal scale. The decimal scale extends through decimal fractions as well as integers, the scale of increase and decrease being uniform from the highest unit of the integer to the lowest unit of the decimal. The names of the units occupying the different places are called the different orders of units; and each group of three orders of units constitutes a period. The left hand period of an integer may contain only one or two figures, or orders of units; it is then called an incomplete period. |