Decimal-point Sentence Examples
Napier thus had complete command over decimal fractions and the use of the decimal point.
The fact that when the base is io the mantissa of the logarithm is independent of the position of the decimal point in the number affords the chief reason for the choice of io as base.
In tables of logarithms of numbers to base io the mantissa only is in general tabulated, as the characteristic of the logarithm of a number can always be written down at sight, the rule being that, if the number is greater than unity, the characteristic is less by unity than the number of digits in the integral portion of it, and that if the number is less than unity the characteristic is negative, and is greater by unity than the number of ciphers between the decimal point and the first significant figure.
The power of io, which occurs as a factor in the tables of both Napier and Byrgius, was rendered necessary by the fact that the decimal point was not yet in use.
A mixed number, the fractional part of which is a decimal fraction, is expressed by writing the integral part in front of the point, which is called the decimal point.Advertisement
Hence the successive figures after the decimal point have the same relation to each other and to the figures before the point as if the point did not exist.
The result is 085.9 = 8 5.9, the position of the decimal point being determined by counting the figures before the decimal points in the original numbers.
Large results - where the number of digits to the left of the decimal point exceeds the current setting of numeric digits.
To Napier seems to be due the first use of the decimal point in arithmetic. Decimal fractions were first introduced by Stevinus in his tract La Disme, published in 1585, but he used cumbrous exponents (numbers enclosed in circles) to distinguish the different denominations, primes, seconds, thirds, &c. Thus, for example, he would have written 123.456 as 123@4050603.
This single instance of the use of the decimal point in the midst of an arithmetical process, if it stood alone, would not suffice to establish a claim for its introduction, as the real introducer of the decimal point is the person who first saw that a point or line as separator was all that was required to distinguish between the integers and fractions, and used it as a permanent notation and not merely in the course of performing an arithmetical operation.Advertisement
Because one carat solitaire diamonds are far more rare than smaller sizes - particularly if they do not have flaws or inclusions - there is a hefty price jump once that decimal point is crossed.
The decimal point is, however, used systematically in the Constructio (1619), there being perhaps two hundred decimal points altogether in the book.
These examples show that Napier was in possession of all the conventions and attributes that enable the decimal point to complete so symmetrically our system of notation, viz.
When the base is to, the logarithms of all numbers in which the digits are the same, no matter where the decimal point may be, have the same mantissa; thus, for example, log 2.5613 =0-4084604, log 25.613 =1.4084604, log 2561300 = 6.4084604, &c.