7. is 5.787787778... a rational or irrational number? explain.
7. is 5.787787778... a rational or irrational number? explain.
Answer
Explanation:
Step1: Recall number - type definitions
A rational number can be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b\neq0$. A non - repeating and non - terminating decimal is irrational, while a repeating decimal is rational.
Step2: Analyze the given decimal
The number $5.787787778...$ is non - repeating. The number of 7s between 8s is increasing ($78$, $778$, $7778$ etc.). Since it is a non - repeating and non - terminating decimal, it cannot be written as a fraction $\frac{a}{b}$ with $a,b\in\mathbb{Z}$ and $b\neq0$.
Answer:
Irrational