Numeration systems are systems used to represent quantities ( Bender et al., 2015 ). For instance, suppose there is a sack of bananas and the owner wants to decide how many bananas are contained in the sack, there will be a need for a numeration system. Throughout history, numerous numeration systems have been created to represent numbers. The most common number system used today is the Hindu-Arabic numerals system. Other numeral systems used are a tally numeral system, Egyptian numerals system, Roman numerals system, Babylonian numerals system and Mayan numerals system. This paper compares and contrasts Hindu-Arabic numeration system with Egyptian numeration system and Roman numeration system according to symbols used, place value, the concept of zero, and additive and (or) multiplicative system.
In Egyptian numeration system, hieroglyphics (picture symbols) are used to represent numbers one, ten, one hundred, one thousand, and so on. These symbols include reed, heel for one, heel bone for ten, coiled rope for one hundred, bent reed for one thousand, pointed finger for ten thousand, and so on. The difference between Egyptian numeration system and the Hindu-Arabic system is that characters used to represent different numbers are different. In Hindu- Arabic numeration system, each number less than the base is represented by a different symbol ( Fuchs et al., 2014 ). For example, numbers less than base ten (one to nine) are represented by different characters. Conversely, in Egyptian numeration system, numbers less than a base are represented by the same character, for example; numbers less than 10 are represented by reed.
Delegate your assignment to our experts and they will do the rest.
Another difference between Egyptian and Hindu-Arabic numeration systems is that in Egyptian numeration systems, there is no symbol for numeral zero, while in Hindu-Arabic system, zero is represented. However, both Egyptian numeration system and Hindu-Arabic system are similar in that they are both based on base ten. Moreover, place values in both systems are represented by the number of objects in the ones, tens, hundreds, and thousands. Addition in both Egyptian and Hindu-Arabic numeration systems is possible and easy for simple addition.
Roman numeration system applies symbols called for one, ten, one hundred, one thousand and so on. For example, one is represented by I, five is represented by V, 10 is represented by X, and fifty is represented by L, and so on ( Hodgson, 2018 ). Both Roman numeration system and Hindu-Arabic system use different symbols to represent numbers. However, the difference is that characters used to represent each number in Roman numeration system are different from those used in the Hindu-Arabic system. In Roman numeration system, the symbols I and V are used to represent numbers from one to nine. Conversely, in Hindu-Arabic numeration systems, numbers less than the base are represented by different symbols; the numbers one to nine have different characters.
Roman numeration system and Hindu-Arabic numeration system also differ in place value and placement system. In the Hindu-Arabic numeration system, take for example a number 19, the 1 in the second position from right represent 10. However, in Roman numeration system, take for example the number VI. The V does not mean a place value but both symbols V and I together represent a whole number, in this case, five plus one which is equal to six. Another contradiction between Roman numeration system and the Hindu-Arabic system is that in Roman numeration system, there is no symbol that represents zero as opposed to the Hindu-Arabic system where zero is represented ( Thanheiser and Melhuish, 2018 ). Both Roman numeration systems and Hindu Arabic numeration system apply addition system. The only difference is that addition in Hindu-Arabic numerals is easier compared to addition in Roman numerals.
References
Bender, A., Schlimm, D., & Beller, S. (2015). The cognitive advantages of counting specifically: A representational analysis of verbal numeration systems in Oceanic languages. Topics in cognitive science , 7 (4), 552-569.
Fuchs, L. S., Geary, D. C., Fuchs, D., Compton, D. L., & Hamlett, C. L. (2014). Sources of individual differences in emerging competence with numeration understanding versus multidigit calculation skill. Journal of educational psychology , 106 (2), 482.
Hodgson, B. R. (2018). Artefacts and Tasks in the Mathematical Preparation of Teachers of Elementary Arithmetic from a Mathematician’s Perspective: A Commentary on Chapter 9. In Building the Foundation: Whole Numbers in the Primary Grades (pp. 227-250). Springer, Cham.
Thanheiser, E., & Melhuish, K. (2018). Leveraging variation of historical number systems to build understanding of the base-ten place-value system. ZDM , 1-17.
