Problems with Teaching Decimal Numbers

2006 ◽  
pp. 119-146
Keyword(s):  
Decimal Numbers

scholarly journals Changing the Order of Factors Does Not Change the Product but Does Affect Students’ Answers, Especially Girls’ Answers

2021 ◽  
Vol 11 (5) ◽  
pp. 201
Author(s):  
Clelia Cascella ◽  
Chiara Giberti ◽  
Giorgio Bolondi
Keyword(s):  
Experimental Design ◽  
Rasch Model ◽  
Achievement Tests ◽  
Mathematical Content ◽  
Probability Sample ◽  
Decimal Numbers ◽  
Common Items ◽  
The Rasch Model ◽  
Grade 8

This study is aimed at exploring how different formulations of the same mathematical item may influence students’ answers, and whether or not boys and girls are equally affected by differences in presentation. An experimental design was employed: the same stem-items (i.e., items with the same mathematical content and question intent) were formulated differently and administered to a probability sample of 1647 students (grade 8). All the achievement tests were anchored via a set of common items. Students’ answers, equated and then analysed using the Rasch model, confirmed that different formulations affect students’ performances and thus the psychometric functionality of items, with discernible differences according to gender. In particular, we explored students’ sensitivity to the effect of a typical misconception about multiplication with decimal numbers (often called “multiplication makes bigger”) and tested the hypothesis that girls are more prone than boys to be negatively affected by misconception.

Decimal Hardware Multiplier

2018 ◽  
pp. 4607-4618
Author(s):  
Mário Pereira Vestias
Keyword(s):  
Number System ◽  
Floating Point ◽  
Binary Number ◽  
Correct Result ◽  
Fundamental Operation ◽  
Floating Point Arithmetic ◽  
Decimal Arithmetic ◽  
Decimal Numbers ◽  
Decimal Multiplication ◽  
Point Arithmetic

IEEE-754 2008 has extended the standard with decimal floating point arithmetic. Human-centric applications, like financial and commercial, depend on decimal arithmetic since the results must match exactly those obtained by human calculations without being subject to errors caused by decimal to binary conversions. Decimal Multiplication is a fundamental operation utilized in many algorithms and it is referred in the standard IEEE-754 2008. Decimal multiplication has an inherent difficulty associated with the representation of decimal numbers using a binary number system. Both bit and digit carries, as well as invalid results, must be considered in decimal multiplication in order to produce the correct result. This article focuses on algorithms for hardware implementation of decimal multiplication. Both decimal fixed-point and floating-point multiplication are described, including iterative and parallel solutions.

Decimal Hardware Multiplier

2019 ◽  
pp. 722-736
Author(s):  
Mário Pereira Vestias
Keyword(s):  
Number System ◽  
Floating Point ◽  
Binary Number ◽  
Correct Result ◽  
Fundamental Operation ◽  
Floating Point Arithmetic ◽  
Decimal Arithmetic ◽  
Decimal Numbers ◽  
Decimal Multiplication ◽  
Point Arithmetic

IEEE-754 2008 has extended the standard with decimal floating-point arithmetic. Human-centric applications, like financial and commercial, depend on decimal arithmetic since the results must match exactly those obtained by human calculations without being subject to errors caused by decimal to binary conversions. Decimal multiplication is a fundamental operation utilized in many algorithms, and it is referred in the standard IEEE-754 2008. Decimal multiplication has an inherent difficulty associated with the representation of decimal numbers using a binary number system. Both bit and digit carries, as well as invalid results, must be considered in decimal multiplication in order to produce the correct result. This chapter focuses on algorithms for hardware implementation of decimal multiplication. Both decimal fixed-point and floating-point multiplication are described, including iterative and parallel solutions.

On the decimal numbers basen

2005 ◽  
Vol 36 (6) ◽  
pp. 601-605
Author(s):  
K.-K. Poon * ◽  
K.-W. Yeung ◽  
W.-C. Shiu
Keyword(s):  
Decimal Numbers

Understanding Decimal Numbers: A Foundation for Correct Calculations

2008 ◽  
Vol 5 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Robyn U Pierce ◽  
Vicki A Steinle ◽  
Kaye C Stacey ◽  
Wanty Widjaja
Keyword(s):  
Decimal Numbers

A Study of the Process of Transformation with Special Emphasis on Its Application to the Division of Decimal Numbers

1947 ◽  
Vol 40 (7) ◽  
pp. 345-354
Author(s):  
Louis E. Ulrich
Keyword(s):  
Mathematics Teacher ◽  
Decimal Numbers

Recently several interesting articles on the division of decimal numbers appeared in The Mathematics Teacher,1 and in various other professional publications referred to in this paper. When a subject is thus widely discussed, it points to a healthy quest on the part of teachers to get at the root of the matter.

Detection of transposition errors in decimal numbers

1967 ◽  
Vol 55 (8) ◽  
pp. 1500-1501 ◽  
Author(s):  
H. Freeman
Keyword(s):  
Decimal Numbers

Decimal numbers and safe interpretation of clinical pathology results

2013 ◽  
Vol 67 (2) ◽  
pp. 179-181 ◽  
Author(s):  
Michael Sinnott ◽  
Robert Eley ◽  
Vicki Steinle ◽  
Mary Boyde ◽  
Leanne Trenning ◽  
...  
Keyword(s):  
Clinical Pathology ◽  
Decimal Numbers
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