The correct description for the number 0.898989... is a repeating decimal. This means that the digits 89 repeat infinitely.
To determine if it is rational or irrational, we need to check if the decimal can be expressed as a fraction or not. By setting x = 0.898989..., we can multiply both sides by 100 to eliminate the repeating portion:
100x = 89.898989...
Subtracting x from both sides:
100x - x = 89.898989... - 0.898989...
99x = 89
Dividing both sides by 99:
x = 89/99
Since x can be expressed as a fraction, it is a rational number.
what is the correct description for this number and is it Rational or Irrational
0.898989…
1 answer