Percents and Decimals

<正>WHEN am I ever going to use this?READING The graphic shows the reasons that students in 6th through 12th grades read.1.Write the percent of students who read for fun as a fraction.2.Write the fraction as a decimal.You have learned that any fraction can be written as a decimal.You can use this fact to write percents as decimals.     

Fractions and Percents

<正>WHEN am I ever going to use this?EDUCATION The table shows the results of a survey in which students were asked to choose methods that make learning new subjects more interesting.1.Shade a 10×10 grid that represents the number of students that chose each method.     

Percents Greater Than 100% and Percents Less Than 1%

<正>Hands-on Mini Lab Work with a partner.·Draw three 10×10 squares on a piece of grid paper.Each large square represents 100%,and each small square represents 1%.·For the first model,use two grids to shade 120 small squares.·For the second model,shade half of one small square on a grid.Use a different color than on the first model.     

Decimals and almost–periodicity

We give conditions on sequences of real numbers so that their leading digit in the decimal-representation appears in an almost-periodic way. Examples are given by solutions of linear recurrences, such as the Fibonacci-sequence. Received: 8 August 2005     

Weak Factorizations,Fractions and Homotopies

We show that the homotopy category can be assigned to any category equipped with a weak factorization system. A classical example of this construction is the stable category of modules. We discuss a connection with the open map approach to bisimulations proposed by Joyal, Nielsen and Winskel. Mathematics Subject Classifications (2000) 18A99, 55P10, 68Q85.JiÍ Rosický: Supported by the Grant Agency of the Czech Republic under the grant 201/02/0148.     

一类有理分式积分的解法

将求有理分式积分的传统待定常数法推广到待定函数法,给出有理分式积分中求部分分式的公式解法,此法可解决一类有理函数的积分问题．     

Simplifying Fractions

<正>Mini Lab Work with a partner.On grid paper,draw the two figures at the right.Both figures should be the same size.Shade 8 out of the 20 squares in one figure.Shade 2 out of the 5rectangles in the other.1.Write a fraction to describe each figure:     

Fractions continues de matrices,convergence et applications

The aim of this article is to give some property of continued fraction with matrices arguments, about their convergence and others applications. At the end of this work, we present a resolution of the Algebraic Riccati Equation by giving an explicit continued fraction development of its solution. This revised version was published online in August 2006 with corrections to the Cover Date.     

Estimating with Fractions

<正>When am I ever going to use this?kites for a kite to have balance while flying,the left and right sides of the horizontal support must each be 2/3 as long as the bottom of the vertical support.Also,the top must be 1/3 as long as the bottom portion.     

Additive Partitions and Continued Fractions

A set S of positive integers is avoidable if there exists a partition of the positive integers into two disjoint sets such that no two distinct integers from the same set sum to an element of S. Much previous work has focused on proving the avoidability of very special sets of integers. We vastly broaden the class of avoidable sets by establishing a previously unnoticed connection with the elementary theory of continued fractions.     

Hurwitz and Tasoev Continued Fractions

The continued fractions studied by Tasoev are not widely known although their characteristics are very similar to those of Hurwitz continued fractions. Recently, the author found several general forms of Tasoev continued fractions, and by applying this method he also obtained some more general forms of Hurwitz continued fractions belonging to so called tanh-type and tan-type. In this paper, we constitute a new class of general forms of Hurwitz continued fractions of e-type. The known continued fraction expansions of e^1/a (a 1), ae^1/a and (1/a)e^1/a are included as special cases. The corresponding Tasoev continued fractions are also derived.     

Hurwitz and Tasoev Continued Fractions

The continued fractions studied by Tasoev are not widely known although their characteristics are very similar to those of Hurwitz continued fractions. Recently, the author found several general forms of Tasoev continued fractions, and by applying this method he also obtained some more general forms of Hurwitz continued fractions belonging to so called tanh-type and tan-type. In this paper, we constitute a new class of general forms of Hurwitz continued fractions of e-type. The known continued fraction expansions of e^1/a (a 1), ae^1/a and (1/a)e^1/a are included as special cases. The corresponding Tasoev continued fractions are also derived.