Research Article

# New Formula for Interval Numbers with Powers of Positive Rational Numbers and Its Properties

@INPROCEEDINGS{10.4108/eai.3-11-2023.2347908, author={Rasi Adishamita and Mashadi Mashadi and Muliana Muliana}, title={New Formula for Interval Numbers with Powers of Positive Rational Numbers and Its Properties}, proceedings={Proceedings of the 3rd Sriwijaya International Conference on Basic and Applied Sciences, SICBAS 2023, November 3, 2023, Palembang, Indonesia}, publisher={EAI}, proceedings_a={SICBAS}, year={2024}, month={8}, keywords={interval arithmetic powers of interval number}, doi={10.4108/eai.3-11-2023.2347908} }

- Rasi Adishamita

Mashadi Mashadi

Muliana Muliana

Year: 2024

New Formula for Interval Numbers with Powers of Positive Rational Numbers and Its Properties

SICBAS

EAI

DOI: 10.4108/eai.3-11-2023.2347908

## Abstract

Development of interval numbers have shown various beliefs regarding the arithmetic and the formulas, one of them is regarding interval numbers with powers. However, there is a deficiency regarding further use for the previous formula of interval number a ̃ with power k where k is a positive integer, that is the basic characteristic of exponents does not apply such as a ̃^k⊗a ̃^l≠a ̃^(k+l). There are some multiplication formulas for interval numbers, but the result of multiplication of an interval number with its invers is not equal to I ̃=[1,1]. Therefore, this article will establish a new formula for interval numbers with powers of positive integers using the new formula of multiplication for interval numbers so that a ̃^k⊗a ̃^l=a ̃^(k+l) apply. Based on this new formula of interval numbers with positive integer powers, formula for interval numbers with fractional powers will also be construct along with the properties that apply to this formula.