Note that the same does Not apply for the 0’s in a number such as this: .710000001

Because the one has value, (even if it’s a tiny value).

For example, if you have a dollar, you could write “I have $1 in my pocket.” Or you could write “I have $1.00 in my pocket.” . . . right? That’s because they’re the same number no matter how many zeroes you write (or don’t write) after a decimal point.

your other number represents .71 billinoths or 71000000/100000000

reducing would leave you with 71/100 again

that is why they are equal

The only way the zeros would hold any meaning is if you were taking a measurement. The figure with all of the zeros would suggest that you have taken your measurement to 8 decimal places (a highly more accurate measurement) versus only 2 decimal places,