Is #0.99999999# a rational, irrational number, natural, whole or integer?

1 Answer
Jun 30, 2015

Answer:

If it stops after 8 decimal places then it is a rational number,

equal to #99999999/100000000#.

If it is a an infinitely recurring patten of #9#'s, then it is equal to #1#.

Explanation:

A rational number is any number that can be expressed as #p/q# for some integers #p# and #q#, with #q != 0#.

#1# is a rational number, being equal to #1/1#. It is also a natural number, whole and integer.

If you are familiar with the 'dot' notation for recurring decimals, then you can write:

#0.dot(9) = 1.0#

If you are not sure this is so, try subtracting:

#1.0 - 0.dot(9)#

and see that you get #0.dot(0) = 0#