1. The problem states that the number $k$ is rounded to two decimal places to give $4.72$. 2. When rounding to 2 decimal places, the actual number $k$ lies within an interval that rounds to $4.72$. 3. The smallest number that rounds up to $4.72$ is $4.715$. This is because numbers from $4.715$ up to just below $4.725$ round to $4.72$. 4. The largest number that rounds down to $4.72$ is just less than $4.725$ but at least $4.715$. 5. Hence, the error interval or the range in which $k$ lies is $$4.715 \leq k < 4.725$$ 6. This interval represents all numbers that round to $4.72$ when rounded to 2 decimal places.