Publisher's Synopsis
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1922 edition. Excerpt: ... CHAPTER IX POWERS OF NUMBERS Powers and Roots The square of any number above 3 has two or more digits: the square of any number above 9 has three or more digits; there is no rule for determining when a series of values, with one more digit in each case than in those of the preceding series begins. Powers and Roots of Decimal and of Mixed Numbers The square of a decimal fraction must have at least two decimal places, and the number of decimal places must be an even number. Thus the square of .2 is .04; the square of .4 is .16; the square of .11 is .0121. It follows from the above that if we have to extract the square root of a single figure decimal, such as .4 or .9, we must add a cipher and use the number with cipher annexed as the first period for the extraction. Thus the square root of .4 has to be taken as the square root of .40, or of .4000, or of .400000, and so on, carrying it out to as many places as desired, always annexing two ciphers, in accordance with the rule for extraction of the square root. The square root of .4 is .632 +; that of .9 is .948 +; the fact that on their face they appear to be single digit squares has nothing to do with the value of their true square roots. Analogous laws for higher powers could be given, but the above is sufficient to illustrate the laws affecting the powers of decimal numbers. It will be seen also that the powers of decimals, when such powers are greater than the first power, and the same applies to fractions, are smaller in value than the original quantities. For corresponding negative powers the reverse is the case; the powers for decimals and fractions are larger than the original quantities, for whole numbers negative powers are smaller. Relations of Numbers and Square Roots of their...
