Jessica thinks of a positive number, $n$, which is less than 1 . She adds this number to its reciprocal and gets 2.9 . Work out the value of $n$. Give your answer as a fraction in its simplest form.

Step 1 ：Given that Jessica thinks of a positive number, $n$, which is less than 1. She adds this number to its reciprocal and gets 2.9. We need to find the value of $n$. We can write the equation as: \[n + \frac{1}{n} = 2.9\]

Step 2 ：First, multiply both sides by $n$ to get rid of the fraction: \[n^2 + 1 = 2.9n\]

Step 3 ：Rearrange the equation to form a quadratic equation: \[n^2 - 2.9n + 1 = 0\]

Step 4 ：Use the quadratic formula to solve for $n$: \[n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Step 5 ：Plug in the values $a = 1$, $b = -2.9$, and $c = 1$ into the quadratic formula and solve for $n$: \[n = \frac{2.9 \pm \sqrt{(-2.9)^2 - 4(1)(1)}}{2(1)}\]

Step 6 ：We have found two possible values for $n$, which are 2.5 and 0.4 (rounded to one decimal place). However, we know that $n$ must be less than 1. Therefore, the value of $n$ that satisfies the given conditions is 0.4.

Step 7 ：Convert the decimal 0.4 to a fraction in its simplest form: \[n = \frac{2}{5}\]

Step 8 ：\(\boxed{\frac{2}{5}}\) is the final answer.