## A treatise on arithmetic in theory and practice for the use of the Irish national schools

### Ireland, Commissioners of National

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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. 1856 Excerpt: ... is exactly 999900 999900 999900 999900: the result obtained by the rule. The same reasoning would hold with any other example. EXERCISES--Key.-page 74. 78. Except where great accuracy is required, it is not necessary to reduce circulating decimals to their equivalent vulgar fractions, and we may add, and subtract them, &c., like other decimals--merely taking care to put down so many of them as will secure sufficient accuracy. 79. Remarks on the nature of Decimals.--It may be noticed here, that no vulgar fraction will give a finite decimal if, when reduced to its lowest terms, the denominator contains any prime factors (factors that are prime numbers--and all the factors, can be reduced to such) except tivos or fives. For neither 10, 100, 1000, &c., nor any multiples of these--as 30, 400, 5000, &c., nor the sum of any of their multiples--as 6420 (6000+400+20), &c., will exactly contain any prime numbers, but 2 or 5. Thus f (considered as 30 tenths an exac quOtient; so also will £ considered as-2 tenths j c,,.,-, 10 tenths 100 hundreds, s for (considered as, or-, fec.) does not contain 7 exactly. For a similar reason \$ will not give an exact quo tient; since (consideredaslgjggor400 hTMdredthS &c.) does not exactly contain 7. 80. A finite decimal must have so many decimal places as will be equal to the greatest number of twos, or fives, contained as factors in the denominator of the original vulgar fraction, reduced to its lowest terms. Thus will give one decimal place; for 2 (found once in its denominator) is contained in 10 (5 X 2); and therefore tenths wijj give some digit (in the tenths' place Sec. II. 77), that is, one decimal as quotient. J C=:2X2-wll give two decimal places; because 2 being found twice as a factor in its denomi...

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