Mathematical principles and computations are used everyday in all aspects of life. Over the years and with major computational advancement, mathematicians have developed simple and easier methods for more challenging and advanced computations with double-precision floating-point accuracy. However, a higher level of numeric precision is required and is more beneficial in certain applications in the scientific and engineering field. This paper presents examples of these applications and analyzes the techniques used to provide high-precision arithmetic. We conclude that high-precision numerical computation softwares are necessary for the modern expansive and demanding problems.