One way to discover fractions is to think about measurement. Anytime we measure something, we will find partial units. For example, measuring the length of a table, we will often find that it is not an exact whole number measurement such as 6 feet. If we were to measure it more carefully, we'd find that the table might be slightly more or less than 6 feet long. In other words, it would be a fraction of a foot more or less than 6 feet.
When measuring something, it is necessary to decide upon the degree of accuracy required. For example, if we were building a house, it might be sufficient to make measurements to the nearest 1/8 inch. On the other hand, a neurosurgeon probably would need more accurate measurements for performing brain surgery.
The required degree of accuracy of measurements depends upon the context or situation.
We need to be able to round numbers so that our estimated answers fall within an acceptable margin of error.