125 km out a total distance of 1000 km of rail track has to be repaired. What percentage of the track is good?
A percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). We often do this because, for example, we can easily and quickly understand the numbers; like we understand how 20¢, 80¢, and $1.00 all relate to one another (notice how "cents" is also related to 100). Percent is usually denoted using the percent sign, "%"; all the % sign means is, "divide me by 100 to get the real number". So 33% is equal to 33 / 100, or 0.33. Notice that to go from the real number, 0.33, to the percentage, we multiply by 100%.
A percent always relates some portion of something to the whole of that something. x = some / whole. So if we have all of something, we get x = whole / whole = 1. To get the percentage, multiply by 100%: 1 x 100% = 100%.
In your problem, the whole track is 1000 km.
The bad portion is 125 km. That means that the good portion is 1000 - 125 = 875 km.
Percentage that is good = part good / whole x 100% = 875 / 1000 x 100%, or
0.875 x 100% = 87.5%