Of course! Let's move forward in a step by step manner.
Before identifying such a number, it is important to understand that 'k^2' means 'k' multiplied by itself and 'k' represents the number itself.
We're looking for a number such that, when we multiply it by itself, the result is less than the original number. It might not be immediately obvious, but let's find out!
Step 1: Identify a potential range of values.
To simplify our search, let's zoom in on the range between 0 and 1. This seems like a good place to start because, in this range, numbers shrink when multiplied.
Step 2: Pick a number from this range.
Now, let's pick a number from this range. Say, 0.5. This number fits within our selected range and is a decent candidate to check against our criteria.
Step 3: Square the selected number.
To check whether the chosen number meets the condition, we need to square it (i.e., multiply it by itself). Remember, squaring a fraction results in a smaller number. So we square 0.5 (that is, 0.5 * 0.5), and the result is 0.25.
Step 4: Compare the square of the number with the original number.
Now, as per our criteria, we have to check if this result (0.25) is less than our original number (0.5).
Indeed, 0.25 is less than 0.5. Hence, the number 0.5 satisfies the condition k^2 < k. So, we have found our number, k = 0.5!
So, to conclude, the number k, which meets the condition k^2 < k, is 0.5.