The claim that folding a piece of paper in half 50 times will result in a thickness equal to 3/4 the distance from the Earth to the Sun is a popular and often-cited analogy, but it is not accurate. In reality, it is impossible to fold a regular piece of paper in half more than about seven to twelve times, depending on various factors such as the size of the paper and its flexibility.
The reason for this limitation is that each time you fold a piece of paper in half, its thickness doubles. After a few folds, the paper becomes significantly thicker, and it becomes increasingly challenging to fold it precisely in half. Eventually, the accumulated thickness prevents further folding.
To illustrate the point, let's assume that the thickness of a typical piece of paper is about 0.1 millimeters. If we fold it in half, it will be 0.2 millimeters thick. After ten folds, the thickness would reach approximately 102.4 millimeters (about 10 centimeters or roughly 4 inches). Continuing this exponential growth, after 20 folds, it would reach approximately 104,857.6 millimeters (about 105 meters or 345 feet), and after 30 folds, it would be around 10.7 kilometers (6.7 miles) thick.
Considering the average distance from the Earth to the Sun, which is about 93 million miles (150 million kilometers), it becomes apparent that even with an unrealistic number of folds, the thickness of the paper would be nowhere near 3/4 of that distance.
The claim you mentioned is often used as an example to highlight the exponential growth of thickness with each fold, but it should not be taken as a literal representation of reality.