Compare the diameter of Earth and the height of the burj Khalifa using exponents. Explain which on is larger and by how many powers

Question

Earth's diameter: 1.27x10^7 meters
Burj Khalifa: 8.28x10^2 meters

Answer 1

To compare the diameter of the Earth and the height of the Burj Khalifa using exponents, we can express both measurements in scientific notation, as you have already done:

• Diameter of Earth: \( 1.27 \times 10^7 \) meters
• Height of Burj Khalifa: \( 8.28 \times 10^2 \) meters

Now, let's express both numbers in powers of ten to see which is larger:

1. Diameter of Earth: \( 1.27 \times 10^7 \) has a base of 10 raised to the power of 7.
2. Height of Burj Khalifa: \( 8.28 \times 10^2 \) has a base of 10 raised to the power of 2.

Next, we can compare the powers of ten directly:

• \( 10^7 \) (Earth) and \( 10^2 \) (Burj Khalifa)

Since \( 7 > 2 \), we conclude that the diameter of the Earth is much larger than the height of the Burj Khalifa.

To determine how many powers of ten larger the Earth's diameter is compared to the Burj Khalifa's height, we subtract the exponent of Burj Khalifa from the exponent of Earth:

\[ 7 - 2 = 5 \]

Thus, the diameter of the Earth is larger than the height of the Burj Khalifa by \( 5 \) powers of ten. Therefore, we can say:

• Earth's diameter \( \approx 10^5 \) times larger than the height of the Burj Khalifa.

Answer 2

Put it into a paragraph and simplify what you said

Answer 3

The diameter of the Earth is approximately \( 1.27 \times 10^7 \) meters, while the height of the Burj Khalifa is \( 8.28 \times 10^2 \) meters. When comparing the two measurements, we see that the Earth's diameter has an exponent of 7, whereas the Burj Khalifa's height has an exponent of 2. This means that the Earth's diameter is larger than the height of the Burj Khalifa by \( 5 \) powers of ten. In simpler terms, the diameter of the Earth is about 100,000 times larger than the height of the Burj Khalifa.