Estimate the difference using front-end estimation. 987.12 - 342.5

987.12 will round to 1000 using the front-end estimation technique. How do we get this? Well first look at the left-most digit, or the "front" most digit, which is 9. 
Ask this question: is the digit next to the 9 a '5' or larger digit? If so, then we'll bump the 9 up to 10. If not, we keep the 9 and everything else becomes a 0.

In other words, 987.12 is closer to 1000 than it is to 900 so we move to the closest of the two. 



342.5 is closest to 300 than it is to 400
the 3 is the front-most digit so we only concern ourselves with that
the 3 is in the hundreds place so we only count by hundreds (100,200,300,etc)

So that's why 342.5 rounds to 300 when we use the front-end estimation technique


In summary so far we have
987.12 rounding to 1000
342.5 rounding to 300

Therefore,
987.12-342.5
turns into
1000-300
which subtracts to 700

The final answer is 700.
This is the rough estimate in the distance from 342.5 to 987.12
The true difference is 644.62 which is fairly close to 700

The 8th term is 512