Asked by LunarLizard
Select the values that are NOT rational numbers, based on your knowledge of decimals. Select TWO answers. (7.NS.2d) 2 pts
(2 points)
Responses
1.6
1.6
-3.714285714285…
-3.714285714285…
12.123123123…
12.123123123…
-2.236067977…
-2.236067977…
0.045895
0.045895
6.1223334444…
Answers
Answered by
GPT-4o mini
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.
1. **1.6** - This is a terminating decimal and can be expressed as \( \frac{16}{10} \), so it is a rational number.
2. **-3.714285714285…** - This is a repeating decimal (the digit "714285" repeats), which can be expressed as a fraction, so it is a rational number.
3. **12.123123123…** - This is also a repeating decimal (the digits "123" repeat), making it a rational number.
4. **-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.
5. **0.045895** - This is a terminating decimal and can be expressed as \( \frac{45895}{1000000} \), making it a rational number.
6. **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:
1. **-2.236067977...**
2. **6.1223334444…** (given its ambiguity and non-termination).
Final selection:
- **-2.236067977…**
- **6.1223334444…**
1. **1.6** - This is a terminating decimal and can be expressed as \( \frac{16}{10} \), so it is a rational number.
2. **-3.714285714285…** - This is a repeating decimal (the digit "714285" repeats), which can be expressed as a fraction, so it is a rational number.
3. **12.123123123…** - This is also a repeating decimal (the digits "123" repeat), making it a rational number.
4. **-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.
5. **0.045895** - This is a terminating decimal and can be expressed as \( \frac{45895}{1000000} \), making it a rational number.
6. **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:
1. **-2.236067977...**
2. **6.1223334444…** (given its ambiguity and non-termination).
Final selection:
- **-2.236067977…**
- **6.1223334444…**
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