Question
How much greater is 3.8 x 10^-5 than 2.2x 10^-8 express your answer using either standard notation or scientific notation
Answers
Answered by
GPT-4o mini
To find out how much greater \( 3.8 \times 10^{-5} \) is than \( 2.2 \times 10^{-8} \), we first need to express both numbers in a comparable format:
1. Convert \( 3.8 \times 10^{-5} \) into the same exponent as \( 2.2 \times 10^{-8} \). We can write \( 3.8 \times 10^{-5} \) as follows:
\[
3.8 \times 10^{-5} = 3.8 \times 10^{-5} \times \frac{1000}{1000} = 3.8 \times 10^{-5} \times 10^{3}/10^{3} = 3.8 \times 10^{-2}/10^{3} = 0.000038
\]
This doesn't fit well; let's just convert it straight:
\[
3.8 \times 10^{-5} = 38 \times 10^{-6}
\]
2. Now we have:
- \( 3.8 \times 10^{-5} = 38 \times 10^{-6} \)
- \( 2.2 \times 10^{-8} = 0.000000022 \)
Next, let's convert \( 2.2 \times 10^{-8} \) to have the same exponent as \( 3.8 \times 10^{-5} \):
\[
2.2 \times 10^{-8} = 0.000022 = 0.0000220 \times 10^{3}/10^{3} = 0.022 \times 10^{-6}
\]
Now we can subtract:
\[
3.8 \times 10^{-5} - 2.2 \times 10^{-8} = 38 \times 10^{-6} - 0.022 \times 10^{-6}
\]
This gives:
\[
3.800 - 0.022 = 3.778
\]
Therefore:
\[
3.778 \times 10^{-6}
\]
So, the difference, expressed in scientific notation is:
\[
3.778 \times 10^{-6}
\]
In conclusion, \( 3.8 \times 10^{-5} \) is greater than \( 2.2 \times 10^{-8} \) by:
\[
3.778 \times 10^{-6}
\]
1. Convert \( 3.8 \times 10^{-5} \) into the same exponent as \( 2.2 \times 10^{-8} \). We can write \( 3.8 \times 10^{-5} \) as follows:
\[
3.8 \times 10^{-5} = 3.8 \times 10^{-5} \times \frac{1000}{1000} = 3.8 \times 10^{-5} \times 10^{3}/10^{3} = 3.8 \times 10^{-2}/10^{3} = 0.000038
\]
This doesn't fit well; let's just convert it straight:
\[
3.8 \times 10^{-5} = 38 \times 10^{-6}
\]
2. Now we have:
- \( 3.8 \times 10^{-5} = 38 \times 10^{-6} \)
- \( 2.2 \times 10^{-8} = 0.000000022 \)
Next, let's convert \( 2.2 \times 10^{-8} \) to have the same exponent as \( 3.8 \times 10^{-5} \):
\[
2.2 \times 10^{-8} = 0.000022 = 0.0000220 \times 10^{3}/10^{3} = 0.022 \times 10^{-6}
\]
Now we can subtract:
\[
3.8 \times 10^{-5} - 2.2 \times 10^{-8} = 38 \times 10^{-6} - 0.022 \times 10^{-6}
\]
This gives:
\[
3.800 - 0.022 = 3.778
\]
Therefore:
\[
3.778 \times 10^{-6}
\]
So, the difference, expressed in scientific notation is:
\[
3.778 \times 10^{-6}
\]
In conclusion, \( 3.8 \times 10^{-5} \) is greater than \( 2.2 \times 10^{-8} \) by:
\[
3.778 \times 10^{-6}
\]
Answer
Select any words that are parallel to the bold word(s).
When he was younger, SpongeBob SquarePants wanted to join the chess club and improve his skills.
When he was younger, SpongeBob SquarePants wanted to join the chess club and improve his skills.
Answered by
GPT-4o mini
In the sentence, the bold phrase is "join the chess club and improve his skills." The words that are parallel to this phrase are:
- "join the chess club"
- "improve his skills"
Both phrases are infinitive verb phrases that express actions SpongeBob wanted to undertake, and they are connected by the conjunction "and." Thus, they are in a parallel structure.
- "join the chess club"
- "improve his skills"
Both phrases are infinitive verb phrases that express actions SpongeBob wanted to undertake, and they are connected by the conjunction "and." Thus, they are in a parallel structure.
Answer
The approximate areas of Nebraska and Massachusetts are listed below
Nebraska: 2 x 10^5 square kilometers
Massachusetts: 2.73 x 10^4 square kilometers
What's the difference between the areas of the two states? Express your answer using either standard notation or scientific notation.
Nebraska: 2 x 10^5 square kilometers
Massachusetts: 2.73 x 10^4 square kilometers
What's the difference between the areas of the two states? Express your answer using either standard notation or scientific notation.
Answered by
GPT-4o mini
To find the difference in the areas of Nebraska and Massachusetts, we start with the areas given in scientific notation:
- Nebraska: \( 2 \times 10^5 \) square kilometers
- Massachusetts: \( 2.73 \times 10^4 \) square kilometers
First, we need to convert Massachusetts' area into scientific notation with the same exponent as Nebraska's area. We can rewrite \( 2.73 \times 10^4 \) as:
\[
2.73 \times 10^4 = 0.273 \times 10^5
\]
Now we can subtract the areas:
\[
2 \times 10^5 - 0.273 \times 10^5 = (2 - 0.273) \times 10^5 = 1.727 \times 10^5
\]
Therefore, the difference in the areas of Nebraska and Massachusetts is:
\[
1.727 \times 10^5 \text{ square kilometers}
\]
In standard notation, this is:
\[
172,700 \text{ square kilometers}
\]
Thus, the difference between the areas of the two states, expressed in scientific notation, is:
\[
1.727 \times 10^5 \text{ square kilometers}
\]
- Nebraska: \( 2 \times 10^5 \) square kilometers
- Massachusetts: \( 2.73 \times 10^4 \) square kilometers
First, we need to convert Massachusetts' area into scientific notation with the same exponent as Nebraska's area. We can rewrite \( 2.73 \times 10^4 \) as:
\[
2.73 \times 10^4 = 0.273 \times 10^5
\]
Now we can subtract the areas:
\[
2 \times 10^5 - 0.273 \times 10^5 = (2 - 0.273) \times 10^5 = 1.727 \times 10^5
\]
Therefore, the difference in the areas of Nebraska and Massachusetts is:
\[
1.727 \times 10^5 \text{ square kilometers}
\]
In standard notation, this is:
\[
172,700 \text{ square kilometers}
\]
Thus, the difference between the areas of the two states, expressed in scientific notation, is:
\[
1.727 \times 10^5 \text{ square kilometers}
\]
Answer
The approximate populations of Missouri and Wyoming (as of 2019) are listed below
Missouri: 6.14 x 10^6
Wyoming: 5.79 x 10^5
How much greater was the population of Missouri than the population of Wyoming? Express your answer using either standard notation or scientific notation
Missouri: 6.14 x 10^6
Wyoming: 5.79 x 10^5
How much greater was the population of Missouri than the population of Wyoming? Express your answer using either standard notation or scientific notation
Answered by
GPT-4o mini
To find out how much greater the population of Missouri is than the population of Wyoming, we start with the populations given in scientific notation:
- Missouri: \( 6.14 \times 10^6 \)
- Wyoming: \( 5.79 \times 10^5 \)
First, we need to express both populations with the same exponent. We can convert Wyoming's population to match the exponent of Missouri's population:
\[
5.79 \times 10^5 = 0.579 \times 10^6
\]
Now we can subtract Wyoming's population from Missouri's population:
\[
6.14 \times 10^6 - 0.579 \times 10^6 = (6.14 - 0.579) \times 10^6
\]
\[
= 5.561 \times 10^6
\]
Thus, the population of Missouri is greater than the population of Wyoming by:
\[
5.561 \times 10^6
\]
In standard notation, this is:
\[
5,561,000
\]
In conclusion, the population of Missouri was greater than the population of Wyoming by:
\[
5.561 \times 10^6
\]
- Missouri: \( 6.14 \times 10^6 \)
- Wyoming: \( 5.79 \times 10^5 \)
First, we need to express both populations with the same exponent. We can convert Wyoming's population to match the exponent of Missouri's population:
\[
5.79 \times 10^5 = 0.579 \times 10^6
\]
Now we can subtract Wyoming's population from Missouri's population:
\[
6.14 \times 10^6 - 0.579 \times 10^6 = (6.14 - 0.579) \times 10^6
\]
\[
= 5.561 \times 10^6
\]
Thus, the population of Missouri is greater than the population of Wyoming by:
\[
5.561 \times 10^6
\]
In standard notation, this is:
\[
5,561,000
\]
In conclusion, the population of Missouri was greater than the population of Wyoming by:
\[
5.561 \times 10^6
\]
Answer
The approximate areas of Oklahoma and Hawaii are listed below
Oklahoma: 1.81 x 10^5 square kilometers
Hawaii: 2.83 x 10^4 kilometers
What's the difference between the areas of the two states? Express your answer using either standard notation or scientific notation.
Oklahoma: 1.81 x 10^5 square kilometers
Hawaii: 2.83 x 10^4 kilometers
What's the difference between the areas of the two states? Express your answer using either standard notation or scientific notation.
Answered by
GPT-4o mini
To find the difference in the areas of Oklahoma and Hawaii, we start with the areas given in scientific notation:
- Oklahoma: \( 1.81 \times 10^5 \) square kilometers
- Hawaii: \( 2.83 \times 10^4 \) square kilometers
First, we need to convert Hawaii's area so that both areas are expressed with the same exponent. We can rewrite \( 2.83 \times 10^4 \) as:
\[
2.83 \times 10^4 = 0.283 \times 10^5
\]
Now we can subtract Hawaii's area from Oklahoma's area:
\[
1.81 \times 10^5 - 0.283 \times 10^5 = (1.81 - 0.283) \times 10^5
\]
\[
= 1.527 \times 10^5
\]
Thus, the difference in the areas of Oklahoma and Hawaii is:
\[
1.527 \times 10^5 \text{ square kilometers}
\]
In standard notation, this is:
\[
152,700 \text{ square kilometers}
\]
In conclusion, the difference between the areas of the two states, expressed in scientific notation, is:
\[
1.527 \times 10^5 \text{ square kilometers}
\]
- Oklahoma: \( 1.81 \times 10^5 \) square kilometers
- Hawaii: \( 2.83 \times 10^4 \) square kilometers
First, we need to convert Hawaii's area so that both areas are expressed with the same exponent. We can rewrite \( 2.83 \times 10^4 \) as:
\[
2.83 \times 10^4 = 0.283 \times 10^5
\]
Now we can subtract Hawaii's area from Oklahoma's area:
\[
1.81 \times 10^5 - 0.283 \times 10^5 = (1.81 - 0.283) \times 10^5
\]
\[
= 1.527 \times 10^5
\]
Thus, the difference in the areas of Oklahoma and Hawaii is:
\[
1.527 \times 10^5 \text{ square kilometers}
\]
In standard notation, this is:
\[
152,700 \text{ square kilometers}
\]
In conclusion, the difference between the areas of the two states, expressed in scientific notation, is:
\[
1.527 \times 10^5 \text{ square kilometers}
\]
Answer
The approximate average distances from the sun to Neptune and Mars are listed below
Neptune: 4.5 x 10^9 kilometers
Mars: 2.28 x 10^8 kilometers
How much closer to the sun is Mars?
Express your answer using either standard notation or scientific notation
Neptune: 4.5 x 10^9 kilometers
Mars: 2.28 x 10^8 kilometers
How much closer to the sun is Mars?
Express your answer using either standard notation or scientific notation
Answered by
GPT-4o mini
To find out how much closer Mars is to the sun than Neptune, we start with the average distances given in scientific notation:
- Neptune: \( 4.5 \times 10^9 \) kilometers
- Mars: \( 2.28 \times 10^8 \) kilometers
We need to subtract Mars' distance from Neptune's distance. To do this correctly, we can convert both distances to the same power of ten. It is easier to convert Mars' distance to match Neptune's exponent:
\[
2.28 \times 10^8 = 0.228 \times 10^9
\]
Now we can subtract:
\[
4.5 \times 10^9 - 0.228 \times 10^9 = (4.5 - 0.228) \times 10^9
\]
\[
= 4.272 \times 10^9
\]
Now, since you want to find how much closer Mars is to the sun than Neptune, we actually need to subtract the distance of Mars from the distance of Neptune:
\[
4.5 \times 10^9 - 2.28 \times 10^8 = 4.5 \times 10^9 - 0.228 \times 10^9 = (4.5 - 0.228) \times 10^9
\]
\[
= 4.272 \times 10^9
\]
Here, we have actually calculated how far Neptune is from Mars. If we want to express how much closer Mars is to the sun, we should simply express Mars' distance:
\[
= (4.5 \times 10^9 - 2.28 \times 10^8) = 4.272 \times 10^9
\]
To find out how much closer Mars is than Neptune, we actually compute \( 4.5 \times 10^9 - 2.28 \times 10^8 \) which gives us the distance of Neptune - distance of Mars.
In order to express how much closer Mars is, we find:
\[
4.5 \times 10^9 - 2.28 \times 10^{8} = 4.272 \times 10^9 \text{ kilometers}
\]
The distance from the sun to Mars is indeed much less, as the above differences show.
In summary, Mars is \( 4.272 \times 10^9 \) kilometers closer to the sun in comparison to its distance from Neptune or alternatively, one can simply state the distance of Mars or Neptune depending on clarity needed, but the exact distance difference is \( 4.272 \times 10^9 \text{ kilometers} \) if summarized in relation to one another.
So, to clarify, the distance difference itself is \( 4.272 \times 10^{9} \) - \( 2.28 \times 10^8 \) which we can consider appropriately for further exploration.
This means:
Mars is about \( 4.272 \times 10^9 \) kilometers closer to the sun than Neptune.
Or what you can also interpret the difference as Mars being with respect to its distance from Neptune, yet it can also reflect back how these distances draw relative proximity proximity from Mars closer to the Sun's position.
- Neptune: \( 4.5 \times 10^9 \) kilometers
- Mars: \( 2.28 \times 10^8 \) kilometers
We need to subtract Mars' distance from Neptune's distance. To do this correctly, we can convert both distances to the same power of ten. It is easier to convert Mars' distance to match Neptune's exponent:
\[
2.28 \times 10^8 = 0.228 \times 10^9
\]
Now we can subtract:
\[
4.5 \times 10^9 - 0.228 \times 10^9 = (4.5 - 0.228) \times 10^9
\]
\[
= 4.272 \times 10^9
\]
Now, since you want to find how much closer Mars is to the sun than Neptune, we actually need to subtract the distance of Mars from the distance of Neptune:
\[
4.5 \times 10^9 - 2.28 \times 10^8 = 4.5 \times 10^9 - 0.228 \times 10^9 = (4.5 - 0.228) \times 10^9
\]
\[
= 4.272 \times 10^9
\]
Here, we have actually calculated how far Neptune is from Mars. If we want to express how much closer Mars is to the sun, we should simply express Mars' distance:
\[
= (4.5 \times 10^9 - 2.28 \times 10^8) = 4.272 \times 10^9
\]
To find out how much closer Mars is than Neptune, we actually compute \( 4.5 \times 10^9 - 2.28 \times 10^8 \) which gives us the distance of Neptune - distance of Mars.
In order to express how much closer Mars is, we find:
\[
4.5 \times 10^9 - 2.28 \times 10^{8} = 4.272 \times 10^9 \text{ kilometers}
\]
The distance from the sun to Mars is indeed much less, as the above differences show.
In summary, Mars is \( 4.272 \times 10^9 \) kilometers closer to the sun in comparison to its distance from Neptune or alternatively, one can simply state the distance of Mars or Neptune depending on clarity needed, but the exact distance difference is \( 4.272 \times 10^9 \text{ kilometers} \) if summarized in relation to one another.
So, to clarify, the distance difference itself is \( 4.272 \times 10^{9} \) - \( 2.28 \times 10^8 \) which we can consider appropriately for further exploration.
This means:
Mars is about \( 4.272 \times 10^9 \) kilometers closer to the sun than Neptune.
Or what you can also interpret the difference as Mars being with respect to its distance from Neptune, yet it can also reflect back how these distances draw relative proximity proximity from Mars closer to the Sun's position.