To determine which number is furthest to the right on the number line, we need to compare the given numbers: \(0.8\), \(-1\), \(\frac{1}{2}\), \(-\frac{1}{4}\), and \(-1.99\).
- \(0.8\) is positive and is greater than all of the negative numbers.
- \(-1\) is negative.
- \(\frac{1}{2}\) is equivalent to \(0.5\), which is also less than \(0.8\).
- \(-\frac{1}{4}\) is equivalent to \(-0.25\), which is also less than \(0.5\) and \(0.8\).
- \(-1.99\) is a negative number that is lower than all the others mentioned.
Out of these numbers, \(0.8\) is the only positive number and is clearly the largest. Therefore, it is located furthest to the right on the number line.
So, the answer is \(0.8\).