Topic
Decimal
About: Decimal is a research topic. Over the lifetime, 2657 publications have been published within this topic receiving 29268 citations. The topic is also known as: base ten & denary.
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TL;DR: Posttest performance by all participants indicated the emergence of equivalence relations between fractions represented as ratios, decimals, and pictures, and limited generalization of fraction-decimal relations was observed.
Abstract: Stimulus control technology was applied to the instruction of fraction ratio (e.g., (1/5)) and decimal (e.g., 0.20) relations, with 7 students who demonstrated difficulty in fraction and decimal tasks. The students were trained to match pictorial representations of fractions (B comparison stimuli) to printed counterpart fraction ratios (A sample stimuli), and to match printed decimals (C comparison stimuli) to pictorial representations of counterpart quantities (B sample stimuli). Posttest performance by all participants indicated the emergence of equivalence relations between fractions represented as ratios, decimals, and pictures. Limited generalization of fraction-decimal relations was observed.
109 citations
TL;DR: This paper examined two days of teacher-led large group discussion in a fifth grade about a mathematical question intended to support student exploration of relationships among fraction and decimal representations and rational numbers, and the teacher's work is conceptualized in terms of actions and practices that coordinate these diverse tools, in constant response to students' concurrent use of them.
Abstract: This case study examines two days of teacher-led large group discussion in a fifth grade about a mathematical question intended to support student exploration of relationships among fraction and decimal representations and rational numbers. The purpose of the analysis is to illuminate the teacher’s work in supporting student thinking through the use of a mathematical question embedded in a position-driven discussion. The focus is an examination of the ways that the emergence of mathematical ideas is partially shaped by complex interactions among the mathematical contents of the question, the inherent properties of the discourse format and participant structure, and the available computational methods. The teacher’s work is conceptualized in terms of actions and practices that coordinate these diverse tools, in constant response to students’ concurrent use of them.
108 citations
27 Jun 2005
TL;DR: A novel design for fixed-point decimal multiplication that utilizes a simple recoding scheme to produce signed-magnitude representations of the operands thereby greatly simplifying the process of generating partial products for each multiplier digit.
Abstract: Decimal multiplication is important in many commercial applications including financial analysis, banking, tax calculation, currency conversion, insurance, and accounting. This paper presents a novel design for fixed-point decimal multiplication that utilizes a simple recoding scheme to produce signed-magnitude representations of the operands thereby greatly simplifying the process of generating partial products for each multiplier digit. The partial products are generated using a digit-by-digit multiplier on a word-by-digit basis, first in a signed-digit form with two digits per position, and then combined via a combinational circuit. As the signed-digit partial products are developed one at a time while traversing the recoded multiplier operand from the least significant digit to the most significant digit, each partial product is added along with the accumulated sum of previous partial products via a signed-digit adder. This work is significantly different from other work employing digit-by-digit multipliers due to the efficiency gained by restricting the range of digits throughout the multiplication process.
104 citations
TL;DR: It is shown that for certain functions it seems desirable to transform the argument to a short range symmetric about 1.0 for both binary and decimal machines.
Abstract: There was the germ of an idea in two previous papers [1, 2] which no one seems to have picked up in almost five years For certain functions it seems desirable to transform the argument to a short range symmetric about 10 I will give examples of this usage for the square root and logarithm function for both binary and decimal machines
104 citations
TL;DR: This paper introduces another number system which may prove useful for manipulating complex numbers on machines, and the binary and octal systems into the limelight.
Abstract: For centuries the decimal number system reigned supreme, except, perhaps, among the Mayan Indians, until the advent of digital computers brought the binary and octal systems into the limelight. This paper introduces another number system which may prove useful for manipulating complex numbers on machines.
103 citations