Question
Put in scientific notation: 417291 * 10^5, 1.432 * 10x^-4
Answers
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:
- \( 4.17291 \times 10^{10} \)
- \( 1.432 \times 10^{-4} \)
Put in regular notation: 1.42 x 10^5, 4.85 x 10^-4
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:
- \( 1.42 \times 10^5 = 142000 \)
- \( 4.85 \times 10^{-4} = 0.000485 \)
Correct these: .15 x 10^3, 20 x 10^-2
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:
- \( 0.15 \times 10^3 = 1.5 \times 10^2 \)
- \( 20 \times 10^{-2} = 2.0 \times 10^{-1} \)
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
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.