Question
Which number is correctly written in scientific notation?
10 times 10^3
2.520 times 10^3
25.20 times 10^3
10 times 10^3
2.520 times 10^3
25.20 times 10^3
Answers
GPT-4o mini
In scientific notation, a number is expressed in the form \( a \times 10^n \) where \( 1 \leq a < 10 \) and \( n \) is an integer.
Let's evaluate the provided options:
1. **10 times 10^3**: This can be expressed as \( 1.0 \times 10^4 \) when converted to scientific notation. It does not fit the standard form since \( a \) is not less than 10.
2. **2.520 times 10^3**: This fits the scientific notation format since \( 2.520 \) is between 1 and 10.
3. **25.20 times 10^3**: This can be expressed as \( 2.520 \times 10^4 \) when converted to scientific notation. It does not fit the standard form since \( a \) is not less than 10.
Hence, the correct answer is **2.520 times 10^3**.
Let's evaluate the provided options:
1. **10 times 10^3**: This can be expressed as \( 1.0 \times 10^4 \) when converted to scientific notation. It does not fit the standard form since \( a \) is not less than 10.
2. **2.520 times 10^3**: This fits the scientific notation format since \( 2.520 \) is between 1 and 10.
3. **25.20 times 10^3**: This can be expressed as \( 2.520 \times 10^4 \) when converted to scientific notation. It does not fit the standard form since \( a \) is not less than 10.
Hence, the correct answer is **2.520 times 10^3**.
yayy
The age of Earth is about 4.6 times 10^9 years old. What is the number in decimal notation?
GPT-4o mini
To convert \( 4.6 \times 10^9 \) years into decimal notation, you move the decimal point in \( 4.6 \) nine places to the right (because of the exponent \( 9 \)).
This gives you:
\[
4.6 \times 10^9 = 4600000000
\]
So, the age of the Earth in decimal notation is **4,600,000,000 years**.
This gives you:
\[
4.6 \times 10^9 = 4600000000
\]
So, the age of the Earth in decimal notation is **4,600,000,000 years**.
yayy
Use scientific notation to compare these numbers: 3,478,660; 34,870,000; 34,786,600. Which number has the greatest value?
GPT-4o mini
To compare the numbers \(3,478,660\), \(34,870,000\), and \(34,786,600\) using scientific notation, we first convert each number into scientific notation:
1. **\(3,478,660\)**:
\[
3,478,660 = 3.47866 \times 10^6
\]
2. **\(34,870,000\)**:
\[
34,870,000 = 3.487 \times 10^7
\]
3. **\(34,786,600\)**:
\[
34,786,600 = 3.47866 \times 10^7
\]
Now we can compare the numbers by looking at their scientific notation:
- \(3.47866 \times 10^6\) (for \(3,478,660\)) is equivalent to \(3.47866\) multiplied by \(1,000,000\).
- \(3.487 \times 10^7\) (for \(34,870,000\)) is equivalent to \(3.487\) multiplied by \(10,000,000\).
- \(3.47866 \times 10^7\) (for \(34,786,600\)) is equivalent to \(3.47866\) multiplied by \(10,000,000\).
Since both \(34,870,000\) and \(34,786,600\) are multiplied by \(10^7\), we will compare the coefficients for these two before making a conclusion:
- \(3.487\) (from \(34,870,000\)) is greater than \(3.47866\) (from \(34,786,600\)).
Thus, the greatest value among the three numbers is **34,870,000**.
1. **\(3,478,660\)**:
\[
3,478,660 = 3.47866 \times 10^6
\]
2. **\(34,870,000\)**:
\[
34,870,000 = 3.487 \times 10^7
\]
3. **\(34,786,600\)**:
\[
34,786,600 = 3.47866 \times 10^7
\]
Now we can compare the numbers by looking at their scientific notation:
- \(3.47866 \times 10^6\) (for \(3,478,660\)) is equivalent to \(3.47866\) multiplied by \(1,000,000\).
- \(3.487 \times 10^7\) (for \(34,870,000\)) is equivalent to \(3.487\) multiplied by \(10,000,000\).
- \(3.47866 \times 10^7\) (for \(34,786,600\)) is equivalent to \(3.47866\) multiplied by \(10,000,000\).
Since both \(34,870,000\) and \(34,786,600\) are multiplied by \(10^7\), we will compare the coefficients for these two before making a conclusion:
- \(3.487\) (from \(34,870,000\)) is greater than \(3.47866\) (from \(34,786,600\)).
Thus, the greatest value among the three numbers is **34,870,000**.
yayy
The density of oxygen is about 1.429 times 10^-4 grams per liter. What number is higher than 1.429 times 10^-4?
GPT-4o mini
To find a number that is higher than \( 1.429 \times 10^{-4} \), you can simply increase the coefficient (the part before the multiplication by the power of ten) while keeping the same exponent.
For example:
- \( 1.5 \times 10^{-4} \) is greater than \( 1.429 \times 10^{-4} \).
- \( 2 \times 10^{-4} \) is also greater than \( 1.429 \times 10^{-4} \).
- \( 1.5 \times 10^{-3} \) (which equals \( 1.5 \times 10^{-4} \times 10 \)) is also higher, but it has a different exponent.
In general, any coefficient greater than \( 1.429 \) multiplied by \( 10^{-4} \) (for example \( 1.43 \times 10^{-4} \) or \( 1.5 \times 10^{-4} \), etc.) will be higher than \( 1.429 \times 10^{-4} \) as long as the exponent remains the same.
For example:
- \( 1.5 \times 10^{-4} \) is greater than \( 1.429 \times 10^{-4} \).
- \( 2 \times 10^{-4} \) is also greater than \( 1.429 \times 10^{-4} \).
- \( 1.5 \times 10^{-3} \) (which equals \( 1.5 \times 10^{-4} \times 10 \)) is also higher, but it has a different exponent.
In general, any coefficient greater than \( 1.429 \) multiplied by \( 10^{-4} \) (for example \( 1.43 \times 10^{-4} \) or \( 1.5 \times 10^{-4} \), etc.) will be higher than \( 1.429 \times 10^{-4} \) as long as the exponent remains the same.
yayy
1.429 times 10^-5
1.429 times 10^-6
4.129 times 10^-4
1.429 times 10^-3
1.429 times 10^-6
4.129 times 10^-4
1.429 times 10^-3
GPT-4o mini
To determine which of the following numbers is higher than \( 1.429 \times 10^{-4} \):
1. \( 1.429 \times 10^{-5} \)
2. \( 1.429 \times 10^{-6} \)
3. \( 4.129 \times 10^{-4} \)
4. \( 1.429 \times 10^{-3} \)
Let's compare each number to \( 1.429 \times 10^{-4} \):
1. **\( 1.429 \times 10^{-5} \)**:
- This is \( 0.0001429 \), which is less than \( 1.429 \times 10^{-4} \) (or \( 0.0001429 \) vs \( 0.001429 \)).
2. **\( 1.429 \times 10^{-6} \)**:
- This is \( 0.00001429 \), which is also less than \( 1.429 \times 10^{-4} \).
3. **\( 4.129 \times 10^{-4} \)**:
- This is \( 0.0004129 \), which is greater than \( 1.429 \times 10^{-4} \).
4. **\( 1.429 \times 10^{-3} \)**:
- This is \( 0.001429 \), which is also greater than \( 1.429 \times 10^{-4} \).
Thus, the numbers that are higher than \( 1.429 \times 10^{-4} \) are:
- **\( 4.129 \times 10^{-4} \)**
- **\( 1.429 \times 10^{-3} \)**
1. \( 1.429 \times 10^{-5} \)
2. \( 1.429 \times 10^{-6} \)
3. \( 4.129 \times 10^{-4} \)
4. \( 1.429 \times 10^{-3} \)
Let's compare each number to \( 1.429 \times 10^{-4} \):
1. **\( 1.429 \times 10^{-5} \)**:
- This is \( 0.0001429 \), which is less than \( 1.429 \times 10^{-4} \) (or \( 0.0001429 \) vs \( 0.001429 \)).
2. **\( 1.429 \times 10^{-6} \)**:
- This is \( 0.00001429 \), which is also less than \( 1.429 \times 10^{-4} \).
3. **\( 4.129 \times 10^{-4} \)**:
- This is \( 0.0004129 \), which is greater than \( 1.429 \times 10^{-4} \).
4. **\( 1.429 \times 10^{-3} \)**:
- This is \( 0.001429 \), which is also greater than \( 1.429 \times 10^{-4} \).
Thus, the numbers that are higher than \( 1.429 \times 10^{-4} \) are:
- **\( 4.129 \times 10^{-4} \)**
- **\( 1.429 \times 10^{-3} \)**
yayy
there is only one answer
GPT-4o mini
I apologize for any confusion in my previous response. Let’s clarify which of the provided options is strictly **higher** than \( 1.429 \times 10^{-4} \):
1. **\( 1.429 \times 10^{-5} \)**: This equals \( 0.00001429 \) (less than \( 1.429 \times 10^{-4} \)).
2. **\( 1.429 \times 10^{-6} \)**: This equals \( 0.000001429 \) (also less).
3. **\( 4.129 \times 10^{-4} \)**: This equals \( 0.0004129 \) (greater than \( 1.429 \times 10^{-4} \)).
4. **\( 1.429 \times 10^{-3} \)**: This equals \( 0.001429 \) (also greater).
Among these options, the only number that is **greater** than \( 1.429 \times 10^{-4} \) is:
- **\( 4.129 \times 10^{-4} \)**
**\( 1.429 \times 10^{-3} \)** is also greater, but if the request is for only one answer, then we have:
**The answer is \( 4.129 \times 10^{-4} \)**.
1. **\( 1.429 \times 10^{-5} \)**: This equals \( 0.00001429 \) (less than \( 1.429 \times 10^{-4} \)).
2. **\( 1.429 \times 10^{-6} \)**: This equals \( 0.000001429 \) (also less).
3. **\( 4.129 \times 10^{-4} \)**: This equals \( 0.0004129 \) (greater than \( 1.429 \times 10^{-4} \)).
4. **\( 1.429 \times 10^{-3} \)**: This equals \( 0.001429 \) (also greater).
Among these options, the only number that is **greater** than \( 1.429 \times 10^{-4} \) is:
- **\( 4.129 \times 10^{-4} \)**
**\( 1.429 \times 10^{-3} \)** is also greater, but if the request is for only one answer, then we have:
**The answer is \( 4.129 \times 10^{-4} \)**.