Multiply & divide by 10, 100, 1000 - Multiply by 10,100,1000
Theory
Multiplying by \(10\), \(100\) or \(1000\) moves every digit to the left — one place for each zero. The digits move; the decimal point stays, and zeros fill any empty whole-number place.
Multiplying by \(10\), \(100\) or \(1000\) makes a number larger, so every digit moves to a higher place: to the left.
Count the zeros to see how far: \(\times 10\) moves \(1\) place, \(\times 100\) moves \(2\), \(\times 1000\) moves \(3\).
The digits move; the decimal point stays still.
Zeros fill any whole-number place left empty, so \(6 \times 100 = 600\).
The number of zeros tells you how many places the digits move to the left.
| Multiply by | Move | Example |
|---|---|---|
| \(\times 10\) | 1 place left | \(34 \rightarrow 340\) |
| \(\times 100\) | 2 places left | \(47 \rightarrow 4700\) |
| \(\times 1000\) | 3 places left | \(1.25 \rightarrow 1250\) |
How to multiply by 10, 100 or 1000
- Count the zeros. One for \(10\), two for \(100\), three for \(1000\).
- Move the digits left. Slide every digit that many places to the left.
- Fill with zeros. Put a zero in any whole-number place left empty.
Move each digit one place left; a zero fills the ones.
| \(34 \times 10\) | \(=\) | \(340\) |
The \(6\) moves to tens, the \(2\) to ones.
| \(6.2 \times 10\) | \(=\) | \(62\) |
Move each digit two places left.
| \(47 \times 100\) | \(=\) | \(4700\) |
They weigh \(1250\) kg.
| \(1.25 \times 1000\) | \(=\) | \(1250\) |
Common pitfalls
Frequently asked questions
What happens when you multiply by 10?
Every digit moves one place to the left, so \(34 \times 10 = 340\). A zero fills the empty ones place.
How do you multiply a decimal by 100?
Move each digit two places left. For \(3.6 \times 100\), the \(3\) goes to hundreds and the \(6\) to tens, giving \(360\).
Why can't you just add a zero for decimals?
Because \(2.5\) and \(2.50\) are equal. Adding a zero does not make it ten times bigger; the digits must move, giving \(25\).
How far do the digits move for 1000?
Three places to the left, one for each zero in \(1000\).
Does the decimal point move?
No. The digits move; the point stays where it is. It only looks like the point moves because the digits slide past it.