Question
                Put in scientific notation: 417291 * 10^5, 1.432 * 10x^-4
            
            
        Answers
                    Answer
            
    Put in regular notation: 1.42 x 10^5, 4.85 x 10^-4
    
                    Answer
            
    Correct these: .15 x 10^3, 20 x 10^-2
    
                    Answer
            
    Let’s look at Rylee(dog). Which weight is most accurate?
A) 15 lbs
B) 15.0 lbs
C) 15.09 lbs
    
A) 15 lbs
B) 15.0 lbs
C) 15.09 lbs
                    Answered by
            GPT-4o mini
            
    To express the numbers in proper scientific notation:
1. For \( 417291 \times 10^5 \):
- First, we need to express \( 417291 \) in scientific notation. We can write it as \( 4.17291 \times 10^5 \).
- Combining that with \( 10^5 \):
\[
4.17291 \times 10^5 \times 10^5 = 4.17291 \times 10^{10}
\]
2. For \( 1.432 \times 10^{-4} \):
- This is already in scientific notation, so it remains as:
\[
1.432 \times 10^{-4}
\]
Thus, the numbers in scientific notation are:
- \( 4.17291 \times 10^{10} \)
- \( 1.432 \times 10^{-4} \)
    
1. For \( 417291 \times 10^5 \):
- First, we need to express \( 417291 \) in scientific notation. We can write it as \( 4.17291 \times 10^5 \).
- Combining that with \( 10^5 \):
\[
4.17291 \times 10^5 \times 10^5 = 4.17291 \times 10^{10}
\]
2. For \( 1.432 \times 10^{-4} \):
- This is already in scientific notation, so it remains as:
\[
1.432 \times 10^{-4}
\]
Thus, the numbers in scientific notation are:
- \( 4.17291 \times 10^{10} \)
- \( 1.432 \times 10^{-4} \)
                    Answered by
            GPT-4o mini
            
    To convert the numbers from scientific notation to regular notation:
1. For \( 1.42 \times 10^5 \):
\[
1.42 \times 10^5 = 1.42 \times 100000 = 142000
\]
So, \( 1.42 \times 10^5 = 142000 \).
2. For \( 4.85 \times 10^{-4} \):
\[
4.85 \times 10^{-4} = 4.85 \times 0.0001 = 0.000485
\]
So, \( 4.85 \times 10^{-4} = 0.000485 \).
In regular notation, the numbers are:
- \( 1.42 \times 10^5 = 142000 \)
- \( 4.85 \times 10^{-4} = 0.000485 \)
    
1. For \( 1.42 \times 10^5 \):
\[
1.42 \times 10^5 = 1.42 \times 100000 = 142000
\]
So, \( 1.42 \times 10^5 = 142000 \).
2. For \( 4.85 \times 10^{-4} \):
\[
4.85 \times 10^{-4} = 4.85 \times 0.0001 = 0.000485
\]
So, \( 4.85 \times 10^{-4} = 0.000485 \).
In regular notation, the numbers are:
- \( 1.42 \times 10^5 = 142000 \)
- \( 4.85 \times 10^{-4} = 0.000485 \)
                    Answered by
            GPT-4o mini
            
    To express the numbers in proper scientific notation, we need to ensure that the coefficient is between 1 and 10.
1. For \( 0.15 \times 10^3 \):
- First, we rewrite \( 0.15 \) in scientific notation:
\[
0.15 = 1.5 \times 10^{-1}
\]
- Now, combine this with \( 10^3 \):
\[
(1.5 \times 10^{-1}) \times 10^3 = 1.5 \times 10^{2}
\]
2. For \( 20 \times 10^{-2} \):
- Rewrite \( 20 \) in scientific notation:
\[
20 = 2.0 \times 10^{1}
\]
- Now, combine this with \( 10^{-2} \):
\[
(2.0 \times 10^{1}) \times 10^{-2} = 2.0 \times 10^{-1}
\]
So the corrected scientific notations are:
- \( 0.15 \times 10^3 = 1.5 \times 10^2 \)
- \( 20 \times 10^{-2} = 2.0 \times 10^{-1} \)
    
1. For \( 0.15 \times 10^3 \):
- First, we rewrite \( 0.15 \) in scientific notation:
\[
0.15 = 1.5 \times 10^{-1}
\]
- Now, combine this with \( 10^3 \):
\[
(1.5 \times 10^{-1}) \times 10^3 = 1.5 \times 10^{2}
\]
2. For \( 20 \times 10^{-2} \):
- Rewrite \( 20 \) in scientific notation:
\[
20 = 2.0 \times 10^{1}
\]
- Now, combine this with \( 10^{-2} \):
\[
(2.0 \times 10^{1}) \times 10^{-2} = 2.0 \times 10^{-1}
\]
So the corrected scientific notations are:
- \( 0.15 \times 10^3 = 1.5 \times 10^2 \)
- \( 20 \times 10^{-2} = 2.0 \times 10^{-1} \)
                    Answered by
            GPT-4o mini
            
    In terms of precision in reporting weight, the most accurate measurement would be the one that conveys the greatest detail about the value. 
Here’s a breakdown of the options:
A) **15 lbs** - This measurement does not indicate any decimal places, so it suggests a rounding to the nearest whole pound.
B) **15.0 lbs** - This measurement implies a precision to one decimal place, indicating that the weight is measured with a degree of accuracy to the nearest tenth of a pound.
C) **15.09 lbs** - This measurement indicates precision to the hundredths place, suggesting that the weight is measured with even greater accuracy.
Based on this analysis, **C) 15.09 lbs** is the most accurate measurement because it provides the greatest level of detail with respect to the dog's weight.
    
Here’s a breakdown of the options:
A) **15 lbs** - This measurement does not indicate any decimal places, so it suggests a rounding to the nearest whole pound.
B) **15.0 lbs** - This measurement implies a precision to one decimal place, indicating that the weight is measured with a degree of accuracy to the nearest tenth of a pound.
C) **15.09 lbs** - This measurement indicates precision to the hundredths place, suggesting that the weight is measured with even greater accuracy.
Based on this analysis, **C) 15.09 lbs** is the most accurate measurement because it provides the greatest level of detail with respect to the dog's weight.
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