exponents question

[kkaman]

If 0< s,t,u<1

then which of the following is close to s+(s+t)10^6+u10^12

1. (s+t+u)10^12
2. 10^12
3. 10^18
OR what else do u think is the answer???

[HallsofIvy]

More to the point, what do YOU think is the answer. Have you tried putting specific values, say s= 1/4, t= 1/2, u= 3/4 and see what happens? The answer will, I suspect, depend upon the relative sizes of s, t, and u. For example, it u= 10-12, then that 1012 term disappears.

[kkaman]

I don't know the answer honestly. I know it all depends on the size of proper fractions also what happens if all the fractions are equal. I'll appreciate if anyone can explain the strategy to solve such questions quickly.
thanks

[CRGreathouse]

The first term is irrelevant and can be dropped for the purpose of estimation. It can't affect the total by even one part in a million.

It's possible for the second term or the third term to dominate, depending on the values of s+t vs. u. For the sum to be close to 10^12, u must be large -- around x to be within a factor of x. (If you want it to be within 1%, u needs to be around 0.99.)

For the sum to be close to s+t+u, s+t must be small compared to u.

[kkaman]

i have gone through the question again and the 4th choice is (s+t+u)10^6. do u think this could be the answer?

[CRGreathouse]

i have gone through the question again and the 4th choice is (s+t+u)10^6. do u think this could be the answer?

It's always an underestimate, but if u is tiny compared to s+t it could be close. Usually it would not be close.