Question

Select the values that are NOT rational numbers, based on your knowledge of decimals. Select TWO answers.

Responses

1.6


-3.714285714285…


12.123123123…

-2.236067977…


0.045895


6.1223334444…

Answer 1

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. **1.6** - Terminating decimal. Rational.
2. **-3.714285714285...** - Repeating decimal (the "714285" repeats). Rational.
3. **12.123123123...** - Repeating decimal (the "123" repeats). Rational.
4. **-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.
5. **0.045895** - Terminating decimal. Rational.
6. **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.