The point never moves
Multiplying by ten does not slide the point along, and it does not add a zero. Every digit steps one column to the left instead. Two things on this chart could be moving; only one of them is.
Where it usually goes wrong
Multiplying by ten is taught as “add a zero”, which is not true of 3.47, and then repaired with “move the decimal point”, which describes the wrong thing moving. The point marks where the ones column ends and it does not go anywhere. It is the digits that change columns.
Try this
- Multiply 3.47 by ten and watch each digit step one column left. The point has not moved.
- Divide by ten twice and watch them step back the other way.
- Switch to a whole number and multiply. “Add a zero” gives the right answer here, which is exactly why the habit survives long enough to break the decimals.
Where this goes next
Metric units, scientific notation and every mental estimate of size run on this, and all three break for anyone who is moving the point.
More about numbers and proportion
- Which Numbers Make A Rectangle?a factor is a width that fills without a gap, and a prime has none but the line
- Two Lines That Move Togethera ratio is what stays true while both quantities change, not a pair of numbers
- Why Four Numbers?the numbers long multiplication makes you add are patches of one rectangle