Do we mean by 3,000 miles?
- A distance between 2,999 and 3,001 miles?
- A distance between 2,990 and 3,010 miles?
- A distance between 2,900 and 3,100 miles?
- A distance between 2,000 and 4,000 miles?
- Without a context, we don’t know what is meant. In each case above, the colored digit is the largest one that is uncertain. As you ascend from bottom to top, the uncertainty decreases and the numbers become increasingly precise.
- Scientific notation will allow us to express these quantities (all are “three thousand”) with the precision or uncertainty being explicit.