To determine which of the given values are not rational numbers, we need to identify whether they can be expressed as a fraction of two integers. Rational numbers can be terminating or repeating decimals, while irrational numbers cannot be expressed as such.
Let's analyze the given values:
- 1.6 - Terminating decimal. Rational.
- -3.714285714285... - Repeating decimal (the "714285" repeats). Rational.
- 12.123123123... - Repeating decimal (the "123" repeats). Rational.
- -2.236067977... - This decimal does not appear to repeat or terminate. This is the decimal representation of the square root of 5, which is an irrational number.
- 0.045895 - Terminating decimal. Rational.
- 6.1223334444... - This decimal does not appear to have a repeating pattern (it seems to be a non-repeating decimal). It is likely irrational.
Thus, the two values that are NOT rational numbers are:
- -2.236067977...
- 6.1223334444...
Those two are irrational numbers.