Now it's 238,856 which is probably more accurate. Now they actually know the distance to the moon to within a few inches. Apollo 11 astronauts left an array of corner mirrors on the moon. A corner mirror is three mirrors arranged like a corner of a box, all at right angles to each other. Such a mirror reflects light directly back toward the source of the light.
Scientists shine a laser at the moon, and measure the time it takes to reflect back.
They can measure this time to within a tiny fraction of a second. The speed of light in a vacuum is a constant. But it is not known very accurately, not anywhere as accurately as the distance to the moon is known. So essentially, they measure the distance to the moon in fractions of a light-second, not in inches or meters. These scientists really measure the distance from their telescope to the Sea of Tranquility.