The mass of the Eiffel Tower is about 9.16 ⋅ 106 kilograms. The mass of the Golden Gate Bridge is 8.05 ⋅ 108 kilograms. Approximately how many more kilograms is the mass of the Golden Gate Bridge than the mass of the Eiffel Tower? Show your work and write your answer in scientific notation. (10 points)
To find the difference in mass between the Golden Gate Bridge and the Eiffel Tower, we need to subtract the mass of the Eiffel Tower from the mass of the Golden Gate Bridge:
Mass difference = Mass of Golden Gate Bridge - Mass of Eiffel Tower
Mass difference = (8.05 ⋅ 10^8 kg) - (9.16 ⋅ 10^6 kg)
Next, we can simplify the calculation by converting both masses to the same power of 10:
Mass difference = (8.05 ⋅ 10^8 kg) - (0.916 ⋅ 10^8 kg)
Mass difference = 8.05 ⋅ 10^8 kg - 0.916 ⋅ 10^8 kg
Mass difference = (8.05 - 0.916) ⋅ 10^8 kg
Mass difference = 7.134 ⋅ 10^8 kg
Therefore, the mass of the Golden Gate Bridge is approximately 7.134 ⋅ 10^8 kilograms more than the mass of the Eiffel Tower.
To find the difference in mass between the Golden Gate Bridge and the Eiffel Tower, we simply subtract the mass of the Eiffel Tower from the mass of the Golden Gate Bridge.
Mass of Golden Gate Bridge - Mass of Eiffel Tower = (8.05 ⋅ 10^8 kilograms) - (9.16 ⋅ 10^6 kilograms)
To subtract these numbers, we need to make the exponents the same. We can do this by converting the mass of the Eiffel Tower to scientific notation with 8.05 ⋅ 10^8 as the exponent.
Mass of Golden Gate Bridge - Mass of Eiffel Tower = (8.05 ⋅ 10^8 kilograms) - (9.16 ⋅ 10^6 ⋅ 10^2 kilograms)
Now we can subtract the two terms:
= (8.05 ⋅ 10^8 kilograms) - (9.16 ⋅ 10^8 kilograms)
= (8.05 - 9.16) ⋅ 10^8 kilograms
= -1.11 ⋅ 10^8 kilograms
Therefore, the mass of the Golden Gate Bridge is approximately 1.11 ⋅ 10^8 kilograms more than the mass of the Eiffel Tower.
To find the difference in mass between the Golden Gate Bridge and the Eiffel Tower, we subtract the mass of the Eiffel Tower from the mass of the Golden Gate Bridge.
Mass of the Golden Gate Bridge = 8.05 ⋅ 10^8 kilograms
Mass of the Eiffel Tower = 9.16 ⋅ 10^6 kilograms
Subtracting the mass of the Eiffel Tower from the mass of the Golden Gate Bridge:
8.05 ⋅ 10^8 kilograms - 9.16 ⋅ 10^6 kilograms = 8.05 ⋅ 10^8 - 9.16 ⋅ 10^6 kilograms
When subtracting numbers in scientific notation, we need to have the same exponent. Therefore, we can rewrite the mass of the Eiffel Tower in scientific notation with an exponent of 8:
9.16 ⋅ 10^6 kilograms = 0.916 ⋅ 10^8 kilograms
Now we can subtract the two masses:
8.05 ⋅ 10^8 kilograms - 0.916 ⋅ 10^8 kilograms = 7.134 ⋅ 10^8 kilograms
Therefore, the mass of the Golden Gate Bridge is approximately 7.134 ⋅ 10^8 kilograms more than the mass of the Eiffel Tower.