Question
Subtract 4.66 x 10 to the negative fifth power - 7.34 x 10 to the negative seventh power
Answers
Answer
The U.S. national debt was $2.9617 x 10 to the thirteenth power in 2021 and $3.98 x 10 to the eleventh power in 1971. Find how much debt increased in the 50-year period.
Answer
The size of a hydrogen atom is about 1.2 x 10 to the negative tenth power m across. The size of an oxygen atom is 0.000000000152 m across. What is the difference between the sizes of these atoms in scientific notation?
Answer
Platelets and red blood cells are components of the blood. A typical platelet and red blood cell have diameters of approximately 2.33 x 10 to the negative sixth power m and 0.0000075 m, respectively. Which blood component has a bigger diameter, and approximately by how much?
Answer
China and India are the most populous countries in the world. China’s population is approximately 1.4 x 10 to the ninth power, while India’s population is approximately 1,400,000,000. How many more people live in China than in India?
Answer
Can you redo that math
Answered by
GPT-4o mini
To subtract \(4.66 \times 10^{-5}\) and \(7.34 \times 10^{-7}\), we first need to express both numbers with the same exponent.
The first step is to convert \(7.34 \times 10^{-7}\) to a form that has the same exponent as \(4.66 \times 10^{-5}\):
\[
7.34 \times 10^{-7} = 0.0734 \times 10^{-5}
\]
Now we can perform the subtraction:
\[
4.66 \times 10^{-5} - 0.0734 \times 10^{-5} = (4.66 - 0.0734) \times 10^{-5}
\]
\[
= 4.5866 \times 10^{-5}
\]
Thus, the result of the subtraction is:
\[
\boxed{4.5866 \times 10^{-5}}
\]
The first step is to convert \(7.34 \times 10^{-7}\) to a form that has the same exponent as \(4.66 \times 10^{-5}\):
\[
7.34 \times 10^{-7} = 0.0734 \times 10^{-5}
\]
Now we can perform the subtraction:
\[
4.66 \times 10^{-5} - 0.0734 \times 10^{-5} = (4.66 - 0.0734) \times 10^{-5}
\]
\[
= 4.5866 \times 10^{-5}
\]
Thus, the result of the subtraction is:
\[
\boxed{4.5866 \times 10^{-5}}
\]
Answered by
GPT-4o mini
To find the increase in U.S. national debt from 1971 to 2021, we need to subtract the debt from 1971 from the debt in 2021.
The debt in 2021 is:
\[
2.9617 \times 10^{13}
\]
The debt in 1971 is:
\[
3.98 \times 10^{11}
\]
Before we can directly subtract these two, we should express both numbers with the same exponent. It's easier to express \(3.98 \times 10^{11}\) in terms of \(10^{13}\):
\[
3.98 \times 10^{11} = 0.0398 \times 10^{13}
\]
Now we can perform the subtraction:
\[
2.9617 \times 10^{13} - 0.0398 \times 10^{13} = (2.9617 - 0.0398) \times 10^{13}
\]
Calculating the subtraction:
\[
2.9617 - 0.0398 = 2.9219
\]
Thus, the increase in debt over the 50-year period is:
\[
2.9219 \times 10^{13}
\]
Now, we box the final answer:
\[
\boxed{2.9219 \times 10^{13}}
\]
The debt in 2021 is:
\[
2.9617 \times 10^{13}
\]
The debt in 1971 is:
\[
3.98 \times 10^{11}
\]
Before we can directly subtract these two, we should express both numbers with the same exponent. It's easier to express \(3.98 \times 10^{11}\) in terms of \(10^{13}\):
\[
3.98 \times 10^{11} = 0.0398 \times 10^{13}
\]
Now we can perform the subtraction:
\[
2.9617 \times 10^{13} - 0.0398 \times 10^{13} = (2.9617 - 0.0398) \times 10^{13}
\]
Calculating the subtraction:
\[
2.9617 - 0.0398 = 2.9219
\]
Thus, the increase in debt over the 50-year period is:
\[
2.9219 \times 10^{13}
\]
Now, we box the final answer:
\[
\boxed{2.9219 \times 10^{13}}
\]
Answered by
GPT-4o mini
To find the difference between the sizes of a hydrogen atom \( (1.2 \times 10^{-10} \text{ m}) \) and an oxygen atom \( (0.000000000152 \text{ m}) \), we first convert the size of the oxygen atom into scientific notation.
The size of the oxygen atom, \(0.000000000152 \text{ m}\), can be expressed as:
\[
1.52 \times 10^{-10} \text{ m}
\]
Now, we can subtract the size of the hydrogen atom from the size of the oxygen atom. First, we ensure both numbers are in the same form:
\[
1.2 \times 10^{-10} \text{ m} \quad \text{and} \quad 1.52 \times 10^{-10} \text{ m}
\]
Now we perform the subtraction:
\[
1.52 \times 10^{-10} - 1.2 \times 10^{-10} = (1.52 - 1.2) \times 10^{-10}
\]
Calculating the subtraction:
\[
1.52 - 1.2 = 0.32
\]
Thus, the difference between the sizes of the hydrogen and oxygen atoms is:
\[
0.32 \times 10^{-10} \text{ m}
\]
To express this in proper scientific notation, we can write:
\[
0.32 \times 10^{-10} = 3.2 \times 10^{-11}
\]
Therefore, the final answer is:
\[
\boxed{3.2 \times 10^{-11} \text{ m}}
\]
The size of the oxygen atom, \(0.000000000152 \text{ m}\), can be expressed as:
\[
1.52 \times 10^{-10} \text{ m}
\]
Now, we can subtract the size of the hydrogen atom from the size of the oxygen atom. First, we ensure both numbers are in the same form:
\[
1.2 \times 10^{-10} \text{ m} \quad \text{and} \quad 1.52 \times 10^{-10} \text{ m}
\]
Now we perform the subtraction:
\[
1.52 \times 10^{-10} - 1.2 \times 10^{-10} = (1.52 - 1.2) \times 10^{-10}
\]
Calculating the subtraction:
\[
1.52 - 1.2 = 0.32
\]
Thus, the difference between the sizes of the hydrogen and oxygen atoms is:
\[
0.32 \times 10^{-10} \text{ m}
\]
To express this in proper scientific notation, we can write:
\[
0.32 \times 10^{-10} = 3.2 \times 10^{-11}
\]
Therefore, the final answer is:
\[
\boxed{3.2 \times 10^{-11} \text{ m}}
\]
Answered by
GPT-4o mini
First, we need to express both diameters in scientific notation for easier comparison.
1. The diameter of a typical platelet is given as:
\[
2.33 \times 10^{-6} \text{ m}
\]
2. The diameter of a typical red blood cell is given as:
\[
0.0000075 \text{ m}
\]
This can be converted to scientific notation:
\[
0.0000075 = 7.5 \times 10^{-6} \text{ m}
\]
Now, let's compare the two components:
- Diameter of a platelet: \(2.33 \times 10^{-6} \text{ m}\)
- Diameter of a red blood cell: \(7.5 \times 10^{-6} \text{ m}\)
Clearly, the red blood cell has a larger diameter.
Next, we find the difference in diameter:
\[
7.5 \times 10^{-6} - 2.33 \times 10^{-6} = (7.5 - 2.33) \times 10^{-6}
\]
Calculating the difference:
\[
7.5 - 2.33 = 5.17
\]
Thus, the difference in diameter is:
\[
5.17 \times 10^{-6} \text{ m}
\]
In conclusion, the blood component with the bigger diameter is the red blood cell, approximately larger by:
\[
\boxed{5.17 \times 10^{-6} \text{ m}}
\]
1. The diameter of a typical platelet is given as:
\[
2.33 \times 10^{-6} \text{ m}
\]
2. The diameter of a typical red blood cell is given as:
\[
0.0000075 \text{ m}
\]
This can be converted to scientific notation:
\[
0.0000075 = 7.5 \times 10^{-6} \text{ m}
\]
Now, let's compare the two components:
- Diameter of a platelet: \(2.33 \times 10^{-6} \text{ m}\)
- Diameter of a red blood cell: \(7.5 \times 10^{-6} \text{ m}\)
Clearly, the red blood cell has a larger diameter.
Next, we find the difference in diameter:
\[
7.5 \times 10^{-6} - 2.33 \times 10^{-6} = (7.5 - 2.33) \times 10^{-6}
\]
Calculating the difference:
\[
7.5 - 2.33 = 5.17
\]
Thus, the difference in diameter is:
\[
5.17 \times 10^{-6} \text{ m}
\]
In conclusion, the blood component with the bigger diameter is the red blood cell, approximately larger by:
\[
\boxed{5.17 \times 10^{-6} \text{ m}}
\]
Answered by
GPT-4o mini
To find out how many more people live in China than in India, we first need to express both populations in the same format for easier comparison.
1. **China’s Population**:
\[
1.4 \times 10^9
\]
2. **India’s Population**:
Given as \(1,400,000,000\), which can also be expressed in scientific notation:
\[
1,400,000,000 = 1.4 \times 10^9
\]
Now we can compare the populations:
- China’s population: \(1.4 \times 10^9\)
- India’s population: \(1.4 \times 10^9\)
Since we see that both populations are identical in this representation, we find that there is no difference in population:
\[
1.4 \times 10^9 - 1.4 \times 10^9 = 0
\]
Thus, there are **no more people living in China than in India** as per the values given.
The final answer is:
\[
\boxed{0}
\]
1. **China’s Population**:
\[
1.4 \times 10^9
\]
2. **India’s Population**:
Given as \(1,400,000,000\), which can also be expressed in scientific notation:
\[
1,400,000,000 = 1.4 \times 10^9
\]
Now we can compare the populations:
- China’s population: \(1.4 \times 10^9\)
- India’s population: \(1.4 \times 10^9\)
Since we see that both populations are identical in this representation, we find that there is no difference in population:
\[
1.4 \times 10^9 - 1.4 \times 10^9 = 0
\]
Thus, there are **no more people living in China than in India** as per the values given.
The final answer is:
\[
\boxed{0}
\]
Answered by
GPT-4o mini
Absolutely! Let's compare the populations of China and India step by step again.
1. **China’s Population**:
\[
1.4 \times 10^9
\]
2. **India’s Population**:
\[
1,400,000,000
\]
This can also be expressed in scientific notation:
\[
1,400,000,000 = 1.4 \times 10^9
\]
Now, let's reevaluate the populations:
- **China**: \(1.4 \times 10^9\)
- **India**: \(1.4 \times 10^9\)
Since both values are the same, we find that:
\[
1.4 \times 10^9 - 1.4 \times 10^9 = 0
\]
This means that **China does not have more people than India** according to the stated populations.
To clarify: Given both numbers represent the same population count, there’s no difference in the populations.
Thus, the answer remains:
\[
\boxed{0}
\]
There is no additional difference between the populations of China and India based on the provided numbers. If you meant to provide different population figures, please share them, and I'd be happy to assist!
1. **China’s Population**:
\[
1.4 \times 10^9
\]
2. **India’s Population**:
\[
1,400,000,000
\]
This can also be expressed in scientific notation:
\[
1,400,000,000 = 1.4 \times 10^9
\]
Now, let's reevaluate the populations:
- **China**: \(1.4 \times 10^9\)
- **India**: \(1.4 \times 10^9\)
Since both values are the same, we find that:
\[
1.4 \times 10^9 - 1.4 \times 10^9 = 0
\]
This means that **China does not have more people than India** according to the stated populations.
To clarify: Given both numbers represent the same population count, there’s no difference in the populations.
Thus, the answer remains:
\[
\boxed{0}
\]
There is no additional difference between the populations of China and India based on the provided numbers. If you meant to provide different population figures, please share them, and I'd be happy to assist!
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