Question
Which set of numbers is arranged in descending order?
1. 7.6 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative thirty power, 7 x 10 to the negative thirty power
2. 7 x 10 to the negative thirty power, 7.2 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative thirty power, 7.6 x 10 to the negative twenty fifth power
3. 7.2 x 10 to the negative thirty power, 7 x 10 to the negative thirty power, 7.6 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative twenty fifth power
4. 7.6 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative thirty power, 7.2 x 10 to the negative twenty fifth power, 7 x 10 to the negative thirty power
1. 7.6 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative thirty power, 7 x 10 to the negative thirty power
2. 7 x 10 to the negative thirty power, 7.2 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative thirty power, 7.6 x 10 to the negative twenty fifth power
3. 7.2 x 10 to the negative thirty power, 7 x 10 to the negative thirty power, 7.6 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative twenty fifth power
4. 7.6 x 10 to the negative twenty fifth power, 7.2 x 10 to the negative thirty power, 7.2 x 10 to the negative twenty fifth power, 7 x 10 to the negative thirty power
Answers
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Answered by
GPT-4o mini
To determine which set of numbers is arranged in descending order, we must compare each number based on its scientific notation.
1. **7.6 x 10^(-25)**
2. **7.2 x 10^(-25)**
3. **7.2 x 10^(-30)**
4. **7 x 10^(-30)**
To compare these effectively, we can rearrange them in terms of their exponent's value as well:
Numbers with larger negative exponents will be smaller than numbers with smaller negative exponents.
In this case:
- \(7.6 x 10^{-25}\) and \(7.2 x 10^{-25}\) are larger than \(7.2 x 10^{-30}\) and \(7 x 10^{-30}\) since -25 is larger than -30.
- Between \(7.6 x 10^{-25}\) and \(7.2 x 10^{-25}\), \(7.6 x 10^{-25}\) is larger.
- Among \(7.2 x 10^{-30}\) and \(7 x 10^{-30}\), \(7.2 x 10^{-30}\) is larger.
**Now, let's list all four numbers in descending order:**
1. \(7.6 x 10^{-25}\)
2. \(7.2 x 10^{-25}\)
3. \(7.2 x 10^{-30}\)
4. \(7 x 10^{-30}\)
Now we can analyze the provided options:
1. \(7.6 x 10^{-25}, 7.2 x 10^{-25}, 7.2 x 10^{-30}, 7 x 10^{-30}\) (Correct order)
2. \(7 x 10^{-30}, 7.2 x 10^{-25}, 7.2 x 10^{-30}, 7.6 x 10^{-25}\) (Incorrect order)
3. \(7.2 x 10^{-30}, 7 x 10^{-30}, 7.6 x 10^{-25}, 7.2 x 10^{-25}\) (Incorrect order)
4. \(7.6 x 10^{-25}, 7.2 x 10^{-30}, 7.2 x 10^{-25}, 7 x 10^{-30}\) (Incorrect order)
Therefore, the correct option representing numbers arranged in descending order is **Option 1: \(7.6 x 10^{-25}, 7.2 x 10^{-25}, 7.2 x 10^{-30}, 7 x 10^{-30}\)**.
1. **7.6 x 10^(-25)**
2. **7.2 x 10^(-25)**
3. **7.2 x 10^(-30)**
4. **7 x 10^(-30)**
To compare these effectively, we can rearrange them in terms of their exponent's value as well:
Numbers with larger negative exponents will be smaller than numbers with smaller negative exponents.
In this case:
- \(7.6 x 10^{-25}\) and \(7.2 x 10^{-25}\) are larger than \(7.2 x 10^{-30}\) and \(7 x 10^{-30}\) since -25 is larger than -30.
- Between \(7.6 x 10^{-25}\) and \(7.2 x 10^{-25}\), \(7.6 x 10^{-25}\) is larger.
- Among \(7.2 x 10^{-30}\) and \(7 x 10^{-30}\), \(7.2 x 10^{-30}\) is larger.
**Now, let's list all four numbers in descending order:**
1. \(7.6 x 10^{-25}\)
2. \(7.2 x 10^{-25}\)
3. \(7.2 x 10^{-30}\)
4. \(7 x 10^{-30}\)
Now we can analyze the provided options:
1. \(7.6 x 10^{-25}, 7.2 x 10^{-25}, 7.2 x 10^{-30}, 7 x 10^{-30}\) (Correct order)
2. \(7 x 10^{-30}, 7.2 x 10^{-25}, 7.2 x 10^{-30}, 7.6 x 10^{-25}\) (Incorrect order)
3. \(7.2 x 10^{-30}, 7 x 10^{-30}, 7.6 x 10^{-25}, 7.2 x 10^{-25}\) (Incorrect order)
4. \(7.6 x 10^{-25}, 7.2 x 10^{-30}, 7.2 x 10^{-25}, 7 x 10^{-30}\) (Incorrect order)
Therefore, the correct option representing numbers arranged in descending order is **Option 1: \(7.6 x 10^{-25}, 7.2 x 10^{-25}, 7.2 x 10^{-30}, 7 x 10^{-30}\)**.
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