# Denominator Sentence Examples

- The
**denominator**sin a is the quantity well known (after Abbe) as the " numerical aperture." - A fractional number is called a proper fraction or an improper fraction according as the numerator is or is not 3 less than the
**denominator**; and an expression 4 such as 24 is called a mixed number. - Generally, to find the sum or difference of two or more fractional numbers, we must replace them by other fractional numbers having the same
**denominator**; it is usually most convenient to take as this**denominator**the L.C.M. - Hence the value of a fraction is not altered by substituting for the numerator and
**denominator**the corresponding numbers in any other column of a multiple-table (§ 36). - Can be applied to n, n', the
**denominator**n remaining unaltered. - The modern system of placing the numerator above the
**denominator**is due to the Hindus; but the dividing line is a later invention. - To add or subtract fractional numbers, we must reduce them to a common
**denominator**; and similarly, to multiply or divide surds, we must express them as power-numbers with the same index. - And that thence every symbolic product is equal to a rational function of covariants in the form of a fraction whose
**denominator**is a power of f x. - When we know the mass of the earth in gravitational measure, its product by the
**denominator**of the fraction just mentioned gives the mass of the sun in gravitational measure. - The pth root of a number (§43) may, if the number is an integer, be found by expressing it in terms of its prime factors; or, if it is not an integer, by expressing it as a fraction in its lowest terms, and finding the pth roots of the numerator and of the
**denominator**separately. **Denominator**factors, that the complete system of the quadratic is composed of the form itself of degree order I, 2 shown by az 2, and of the Hessian of degree order 2, o shown by a2.- 1 A2B' Where The
**Denominator**Factors Indicate The Forms Themselves, Their Jacobian, The Invariant Of The Quadratic And Their Resultant; Connected, As Shown By The Numerator, By A Syzygy Of Degreesorder (2, 2; 2). - Fraction in its Lowest Terms.-A fraction is said to be in its lowest terms when its numerator and
**denominator**have no common the more correct method is to write it a: b. - Hence we can treat the fractional numbers which have any one
**denominator**as 0 o constituting a number-series, as shown in the 2 adjoining diagram. - A simple fraction with ioo for
**denominator**, can be expressed by writing the two figures of the numerator (or, if there is only one figure, this figure preceded by o) with a dot or " point " before them; thus 76 means 76%, or 17 -6 6 o. - A fraction written in this way is called a decimal fraction; or we might define a decimal fraction as a fraction having a power of To for its
**denominator**, there being a special notation for writing such fractions. - The Romans commonly used fractions with
**denominator**12; these were described as unciae (ounces), being twelfths of the as (pound). - Hindu treatises on arithmetic show the use of fractions, containing a power of io as
**denominator**, as early as the beginning of the 6th century A.D. - Descending series of the semi-convergent class, available for numerical calculation when u is moderately large, can be obtained from (12) by writing x=uy, and expanding the
**denominator**in powers of y. - The frequency ratios in the diatonic scale are all expressible either as fractions, with i, 2, 3 or 5 as numerator and
**denominator**, or as products of such fractions; and it may be shown that for a given note the numerator and**denominator**are smaller than any other numbers which would give us a note in the immediate neighbourhood. - Where the
**denominator**stands for the same homogeneou~ quadratic function of the qs that T is for the is. - Must have a least value, which is moreover positive, since the numerator and
**denominator**are both essentially positive. - Denote the unsteadiness of the motion of the flywheel; the
**denominator**S of this fraction is called the steadiness. - Every convergent is a nearer approximation to the value of the whole fraction than any fraction whose
**denominator**is less than that of the convergent. - If we write 74 in the form 47 we may say that the value of a fraction is not altered by multiplying or dividing the numerator and
**denominator**by any number. - Hence, so long as the
**denominator**remains unaltered, we can deal with, exactly as if they were numbers, any operations being performed on the numerators. - - A fraction (or fractional number), the numerator or
**denominator**of which is a fractional number, is called a complex fraction (or fractional number), to distinguish it from a simple fraction, which is a fraction having integers for numerator and**denominator**. - Thus to divide by a fractional number we must multiply by the number obtained by interchanging the numerator and the
**denominator**, i.e. - By means of the present and the preceding sections the rule given in § 63 can be extended to the statement that a fractional number is equal to the number obtained by multiplying its numerator and its
**denominator**by any fractional number. - Except in the case of - and 2, the fraction was expressed by the
**denominator**, with a special symbol above it. - The Babylonians expressed numbers less than r by the numerator of a fraction with
**denominator**60; the numerator only being written. - Then the
**denominator**of the fraction, the numerical aperture, must be correspondingly increased, in order to ascertain the real resolving power. - The modern method is to deal with fractions which have ioo as
**denominator**; such fractions are called percentages. - A different method was used by Diophantus, accents being omitted, and the
**denominator**being written above and to the right of the numerator. - B,, Y the numerator (or
**denominator**) of the last preceding term by the corresponding quotient and adding the numerator (or**denominator**) of the term before that. - In the sexagesimal system the numerators of the successive fractions (the
of which were the successive powers of 60) were followed by', ", "', ", the**denominators****denominator**not being written. - In the case of fractions of the more general kind, the numerator was written first with ', and then the
**denominator**, followed by ", was written twice. - If the
**denominator**of the fraction, when it is in its lowest terms, contains any other prime factors than 2 and 5, it cannot be expressed exactly as a decimal; but after a certain point a definite series of figures will constantly recur. - (iv) Each convergent is nearer to the true value than any other fraction whose
**denominator**is less than that of the convergent. - We can so determine these n covariants that every other covariant is expressed in terms of them by a fraction whose
**denominator**is a power of the binary form. - If this arrangement is expressed by a fraction, the numerator of which indicates the number of turns, and the
**denominator**the number of internodes in the spiral cycle, the fraction will be found to represent the angle of divergence of the consecutive leaves on the axis. - For the application of continued fractions to the problem " To find the fraction, whose
**denominator**does not exceed a given integer D, which shall most closely approximate (by excess or defect, as may be assigned) to a given number commensurable or incommensurable," the reader is referred to G. - Again, for the cubic, we can find A3(z) - -a6z6 1 -az 3.1 -a 2 z 2.1 -a 3 z 3.1 -a4 where the ground forms are indicated by the
**denominator**factors, viz.: these are the cubic itself of degree order I, 3; the Hessian of degree order 2, 2; the cubi-covariant G of degree order 3, 3, and the quartic invariant of degree order 4, o. - This
**denominator**must, if the fractions are in their lowest terms (§ 54), be a multiple of each of the; it is usually most convenient that it should be their L.C.M.**denominators**