To compare the diameter of Earth and the height of the Burj Khalifa using exponents, we first need to establish their respective measurements:
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Diameter of Earth: The average diameter of Earth is approximately \(12,742\) kilometers, which can be expressed in scientific notation as: \[ 1.2742 \times 10^4 \text{ km} \]
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Height of the Burj Khalifa: The height of the Burj Khalifa is about \(828\) meters. To express this in kilometers, we convert meters to kilometers by dividing by \(1000\): \[ 828 \text{ m} = 0.828 \text{ km} = 8.28 \times 10^{-1} \text{ km} \]
Now we can compare the two numbers in terms of exponents:
- Diameter of Earth: \(1.2742 \times 10^4\)
- Height of Burj Khalifa: \(8.28 \times 10^{-1}\)
Comparison:
To compare these quantities, we can look at their powers of ten:
- The diameter of Earth is on the order of \(10^4\).
- The height of the Burj Khalifa is on the order of \(10^{-1}\).
Which is larger?
Clearly, \(10^4\) is significantly larger than \(10^{-1}\).
By how many powers of 10?
To find out how many powers of ten one is larger than the other, we can subtract the exponents:
\[ 10^4 - 10^{-1} = 4 - (-1) = 4 + 1 = 5 \]
Thus, the diameter of Earth is larger than the height of the Burj Khalifa by 5 powers of ten.
In conclusion, the diameter of the Earth is much larger than the height of the Burj Khalifa, specifically by a factor of \(10^5\), or 100,000 times larger.
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