Why do you need to line up the decimal point before comparing and ordering numbers with that small?

Answer 1

Magnitude is very important.

An example should make it clear:

600.0 is bigger than 60.00. 600 and 60.

.0006000 is smaller than .00600. 6/1000 and 6/100

Every zero on the left of the decimal makes digits further to the left ten times bigger. Every zero to the right makes digits further to the right ten times smaller.

Every number you write with a decimal really sits on top of 0000.0000, with the zeroes continuing forever in both directions. We just don't write most of them because they don't tell us anything useful- we only care about the digits that are not zero, and how far away from the decimal they are. You obviously can't skip writing ALL zeroes because then you would lose track of the decimal point for lots of numbers.

There's another way of writing these numbers when you do have a large number of important zeroes though.

Scientific notation keeps track of the actual decimal in a different way.

1.23*10^3 means there are 3 zeroes to the left of the decimal, giving you 1230.

4.567*10^-2 means two zeros to the right, giving you .04567

Since the 4 was in the ones column it goes on the last zero.

In this way we can write numbers like 2.99*10^-12 or 6.02*10^23 without taking up a lot of room to write all the zeroes.