Question

The mass of a freight train is 9.98 ⋅ 106 kilograms. The mass of an aircraft carrier is 7.3 ⋅ 107 kilograms. Approximately how many more kilograms is the mass of an aircraft carrier than the mass of a freight train? Show your work and write your ans

Answer 1

Of those 2 numbers, the one to the 7th power is bigger, which is the aircraft. To find out how much heavier the aircraft is than the train, we have to subtract those numbers. But we have a problem, because in order to subtract numbers in scientific notation, we have to have the exponents on the 10's be the same and they're not. So we need to work on that. We want the power of 6 to become the power of 7, since we are subtracting the power of 6 on the train from the power of 7 on the aircraft. To get 6 to become 7 we add one. That means that we can rewrite the problem as
`7.7e*10^7-[(10^6*10^1)(...)]`. I purposely stopped there to explain what happens in the rest of that problem where the dots are. If we have to ADD in "10 to the first" to get the 6 to become a 7, we also have to subtract it away to keep the equation in balance. So to finish off the problem we have
`7.73*10^7-[(10^6*10^1)(9.98*10^(-1))]`.
`9.98*10^(-1)=.998`, so what we have after that simplification is
`7.73*10^7-.998*10^7`. Now that the powers are the same on the bases we can subtract 7.73 - .998 which is
`6.732*10^7`. That's how much heavier the aircraft is than the train.