An elementary treatise on arithmetic, in theory and practice; adapted to the instruction of youth in schools and academies in the United States - Softcover

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1827 Excerpt: ...seven tenths, no hundredths, and nine thousandths. 118. Hence, the values of figures in decimals, as well as in whole numbers, are increased in a tenfold ratio by removing them one place towards the left hand, and diminished in the same ratio by removing them one place to the right. Thus, in the decimal.004, by removing the point one place to the right, and consequently the figures of the decimal one place to the left, we have.04, which denotes Tfo, or T$£o, and is ten times the given fraction, TAr, Dut by iQ" troducing a cipher after the point, which removes the figures a place to the right, we have.001)4, or tt&oo which is evidently only a tenth part of the given fraction Jjjj, or ToVW From these principles it will appear evident, that: 119. A decimal is multiplied by 10, if the separating point be removed one place towards the right hand; by 100, if two places; by 1000, if three places, &c.; vacant places, when such occur, being supplied in both cases by ciphers. Thus,.7248X10=7.248, or 7TVA; 6.347X100= « 634-7; 6-3X1000=6300. Also, 78'33-r-l 0=7.833; 736-j-100='00736; 7.3-j-100='073, &c. It appears from the same principles, that: 120. The value of a decimal is not changed by annexing a cipher to the end of it, nor by taking one away, as in each case the significant figures retain the same positions in relation to the separating point. Thus,.50=.5=.500 each being equivalent to one half. From this view of the nature of decimal fractions, it appears, that v there is in every respect the closest resemblance between them and whole o Exercises in Notation and Numeration of Decimal Fractions. Write the following fractions according to the notation of decimal fractions: 1. Three hundred and six ten-thousandths. 2. Three hundred-thousa...

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