# 125 km out a total distance of 1000 km of rail track has to be repaired. What percentage of the track is good?

kjcdb8er | Certified Educator

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%

iambarney155 | Student

To answer this Q you divide 125 km by 1000 because you have one thousand kilometers and 125 are damaged and that will give you will get .125, you will multiply that by 100 and that will give you 12.5 which is your final answer.

12.5 percent has to be repaired