Answer:
688/999.
Explanation:
To express the repeating decimal 0.68888888888... as a rational number, you can set it up as an equation and solve for the fraction.
Let x = 0.68888888888...
Now, we want to remove the repeating part by multiplying x by an appropriate power of 10. In this case, we'll multiply by 10 to the power of the number of decimal places in the repeating part:
1000x = 688.88888888...
Now, we'll subtract x from 1000x to eliminate the repeating part:
1000x - x = 688.88888888... - 0.68888888888...
999x = 688
Now, divide both sides by 999 to isolate x:
x = 688 / 999
So, the repeating decimal 0.68888888888... can be expressed as the rational number 688/999.