Measures are approximate because of human error and the slight variation of items being measured. For smaller units of measure, it’s hard to get the exact same measurement every time for items being made. For example, if someone used two similar measuring instruments to measure an item such as an electric outlet or fence post, each of those instruments would give a slightly different measurement for that item.
Measurements Contain Error All measurements contain some error. For example GPS measurements are not completely accurate. For the purpose of following directions from one place to another, GPS instruments are quite reliable. However, for a civil engineer a GPS instrument can assist with designing a road, but it can’t produce the exact measurements needed to complete the design. When a civil engineer designs a new road, they need to use various measurements to make the road level and line up in a straight line. The measurements the engineer uses on the ground would need to be smaller than the measurement used by the GPS system. (ITC)
Differences in Unit Measurement Affect Precision The GPS measurements are based off of satellite, given coordinates. Although these measurements are close to the real measure, there is still a degree of margin. For example, rumor has it that a cruise missile could hit anywhere on the planet with a degree of error of a basketball. (ITC). This is a possibility because a GPS system is measuring the whole earth and then breaking what you are measuring it into smaller measurements.
When Mathematical Precision is Not Always Possible An example of when precision is needed, but is not always mathematically possible every time, is surgery. Surgeons need to perform the surgery with what is in front of them. It is not possible to get a precise mathematical measurement on each person’s body to assist the surgeon to make the right incisions in the exact place for each person, since all bodies are different. Many types of surgical incisions need to be done by sight and experience by a physician. Another example of when precision is needed, but is not always mathematically possible every time, is when mowing the lawn. The entire lawn needs to be cut precisely to make it look nice, but you may cut the lawn more than one time each week to make it look nice. However, it isn’t always possible to know the number of times to cut the lawn to have it look precisely the same each time, because of the growth rate of the grass. The person mowing the lawn determines the number of times the lawn must be cut by how it looks.
When Mathematical Precision is Important
An example of when mathematical precision is needed is when an engineer surveys a road. The slope of the ground and the new road's surface area of the road need to be calculated in order for the new road to be level. Another example of when mathematical precision is needed is when a city’s water system is created or extended. The city needs to figure out the water capacity to handle all the houses and other buildings in the area being served.
