Multiply & divide decimals by 10, 100, 1000 - Multiply by 10,100,1000
Theory
To multiply a decimal by 10, 100 or 1000, move every digit one, two or three places to the left. The point stays where it is — it is the digits that change columns.
Multiplying makes a number larger, so each digit takes a bigger place value and moves left.
Multiply by \(10\) for one place, \(100\) for two places and \(1000\) for three places.
The decimal point does not move; the digits change columns. Fill any empty place with a zero.
The number you multiply by sets how many places the digits move.
| Multiply by | Places left | Example |
|---|---|---|
| \(10\) | 1 | \(0.5 \times 10 = 5\) |
| \(100\) | 2 | \(2.34 \times 100 = 234\) |
| \(1000\) | 3 | \(0.06 \times 1000 = 60\) |
How to multiply by 10, 100 or 1000
- Count the zeros: \(10\) is one place, \(100\) two, \(1000\) three.
- Move every digit that many places to the left.
- Fill any empty place with a zero.
The \(5\) tenths become \(5\) ones.
| \(0.5 \times 10\) | \(=\) | \(5\) |
Move every digit two places left.
| \(2.34 \times 100\) | \(=\) | \(234\) |
The \(6\) hundredths become \(6\) tens.
| \(0.06 \times 1000\) | \(=\) | \(60\) |
There are 100 cm in 1 m.
| \(1.25 \times 100\) | \(=\) | \(125\text{ cm}\) |
Common pitfalls
Frequently asked questions
What happens when you multiply a decimal by 10?
Every digit moves one place to the left, taking a place value ten times larger. \(0.5 \times 10 = 5\).
Does the decimal point move?
No. The point stays where it is; the digits move to bigger places. It looks like the point moves, but it is the digits that shift.
How many places for 1000?
Three places to the left, because \(1000\) has three zeros. \(0.06 \times 1000 = 60\).
Why not just add zeros to the end?
Adding zeros after the decimal point adds no value. \(0.4 \times 100 = 40\), not \(0.400\).