Mental Irrational Values

Worksheet Description

This worksheet is designed to help students determine whether a given rational number is expressible as a terminating decimal without actually performing the division. The rule provided states that a rational number p/q is expressible as a terminating decimal if the prime factors of q are 2 and 5 only. Students must analyze the denominators of the given fractions to see if they meet this criterion. The task involves understanding prime factorization and applying this knowledge to the concept of decimal representation of rational numbers.

The worksheet aims to teach students about the properties of rational numbers and their decimal expansions. It reinforces the concept that only those fractions with denominators that have prime factors of 2 and/or 5 will result in terminating decimals when written in decimal form. Through this exercise, students learn how to examine and break down denominators into their prime factors, deepening their understanding of number theory. Moreover, the worksheet illustrates a practical application of prime factorization, showing how it can predict the type of decimal expansion a fraction will have without the need for long division.