To determine which values are NOT rational numbers, we need to identify the decimals that are either non-repeating and non-terminating or cannot be expressed as the ratio of two integers.
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1.6 - This is a terminating decimal and can be expressed as \( \frac{16}{10} \), so it is a rational number.
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-3.714285714285… - This is a repeating decimal (the digit "714285" repeats), which can be expressed as a fraction, so it is a rational number.
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12.123123123… - This is also a repeating decimal (the digits "123" repeat), making it a rational number.
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-2.236067977… - This is a non-repeating, non-terminating decimal. It is the decimal representation of \( -\sqrt{5} \), which cannot be expressed as a fraction, so it is NOT a rational number.
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0.045895 - This is a terminating decimal and can be expressed as \( \frac{45895}{1000000} \), making it a rational number.
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6.1223334444… - This is a non-terminating decimal, but it appears to have a pattern of repeating digits (the "4444…" suggests repetition of 4). However, with the lack of a clear repeating group, it's not definitively repeating and could represent an irrational number.
Based on this analysis, the two decimal values that are NOT rational numbers are:
- -2.236067977...
- 6.1223334444… (given its ambiguity and non-termination).
Final selection:
- -2.236067977…
- 6.1223334444…