Question

Determine if 0.393993999399993999993..... is rational or irrational and give a reason for your answer.

Answer 1

The number 0.393993999399993999993... is rational because it can be expressed as a ratio of two integers.

Step-by-step explanation:

The number 0.393993999399993999993... is rational. To determine this, let's set x = 0.393993999399993999993... and 1000x = 393.993999399993999993.... Subtracting x from 1000x gives us 999x = 393, so x = 393/999.

This fraction can be simplified to 131/333.

Since x can be expressed as a ratio of two integers, it is rational.