is -.06006000600006 a rational or irrational number
If the number is
-.06006000600006....
I.e. the decimal expansion does not terminate and the number of zeroes increases by one between the sixes, then the number is irrational because the decimal expansion of a rational number must either terminate or be periodic.
I do not know of any trick to prove it rational, so suspect it is irrational.
To determine if the number -.06006000600006 is rational or irrational, we need to check if it can be expressed as a quotient of two integers (i.e., in the form a/b, where a and b are integers and b is not zero).
In this case, we can see that the number can be written as -6006000600006/100000000000000. Both the numerator and denominator are integers, and the denominator is not zero.
Therefore, the number -.06006000600006 is rational.
To determine if the number -.06006000600006 is rational or irrational, we need to analyze its nature.
A rational number can be expressed as a ratio of two integers, where the denominator is not zero. On the other hand, an irrational number cannot be expressed as a simple fraction or ratio.
To ascertain if -.06006000600006 is rational or irrational, we can examine its decimal representation. If the decimal representation terminates or repeats, it is rational. However, if the decimal representation continues indefinitely without any pattern, it is irrational.
Unfortunately, the given number, -.06006000600006, does not terminate or repeat. Instead, it has a pattern of repeating zeros. Therefore, we can conclude that -.06006000600006 is a rational number.
Please note that if you want to be more precise with the classification of the number, it would be helpful to convert it into a simpler fraction by removing the repeating digits.