302,303 views
12 votes
12 votes
Is 8.888... a rational number?

User Tafaust
by
2.5k points

1 Answer

20 votes
20 votes

Answer: Yes it's a rational number

=================================================

Step-by-step explanation:

Since the decimal repeats itself infinitely (the 8s go on forever), this is one sign that we have a rational number.

Rational numbers always have some kind of infinitely repeating pattern when we convert them to decimal form.

---------------------

Extra info (optional section)

If you want to determine what this number is equal to, then let's say that

x = 8.8888...

Multiplying both sides by 10 gets us

10x = 88.888....

Now we'll subtract the two equations

The 10x-x becomes 9x while the 88.8888...-8.8888... turns into 80

We're left with 9x = 80 which solves to x = 80/9

Therefore, 80/9 = 8.8888.... showing that we have a rational number

Any rational number is basically a fraction of two whole numbers.

User Mathijs Rutgers
by
3.1k points