Lab: The Decimal Shift Machine
Watch digits slide across the place-value chart as you multiply or divide by 10, 100, and 1000 — the visual behind every shift rule.
Place-value shift machine
3.45
digits
decimal point (fixed)
Try it
Challenge: use the machine to compute 3.45 × 100.
Press the × 100 button, then type the result.
What to notice: the point never moves — the digits slide left when you multiply and right when you divide. “Moving the point” is just a shortcut for describing digit motion.
Why it works
Each column is ten times the column to its right. Multiplying by 10 promotes every digit one column left (3 ones become 3 tens). Dividing demotes them right. The decimal point is nailed to the chart between the ones and tenths columns.