Multiplying and dividing by 10 and 100
Maths · Key Stage 2 · The School
It is not about adding a zero
You may have heard: to multiply by 10, just add a zero. That works for whole numbers, but it is the wrong way to think about it. What is really happening is that every digit moves one place to the left. The "add a zero" trick breaks completely once decimals appear. Understanding the real rule now saves confusion later, once decimals become part of every calculation.
Digits sliding left
Take 34. Multiply by 10 and the 3 and the 4 both slide one column to the left. The 3 moves from tens into hundreds. The 4 moves from ones into tens. An empty ones column needs a zero to hold its place. That gives 340. Picture a place-value grid with each digit sitting in its own column. Sliding every digit one column left is exactly what multiplying by 10 does.
Sliding the other way
Dividing by 10 slides every digit one place to the right instead. Take 340. The 3 moves back into tens. The 4 moves back into ones. Nothing is left to fill the ones column from, so the answer is simply 34. Multiplying by 100 slides digits two places, not one.
Where the zero trick fails
Try 3.4 multiplied by 10 using the zero trick: you might write 3.40, which looks unchanged. That is wrong. Slide every digit one place left instead: the 3 moves into tens, the 4 moves into ones. The answer is 34. The digit-sliding method gives the right answer every time, for whole numbers and decimals alike.