Multiply & divide decimals by 10, 100, 1000 - Divide by 10,100,1000
Theory
To divide a decimal by 10, 100 or 1000, move every digit one, two or three places to the right. The point stays where it is — it is the digits that change columns.
Dividing makes a number smaller, so each digit takes a smaller place value and moves right.
Divide 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 divide by sets how many places the digits move.
| Divide by | Places right | Example |
|---|---|---|
| \(10\) | 1 | \(5 \div 10 = 0.5\) |
| \(100\) | 2 | \(23 \div 100 = 0.23\) |
| \(1000\) | 3 | \(6 \div 1000 = 0.006\) |
How to divide by 10, 100 or 1000
- Count the zeros: \(10\) is one place, \(100\) two, \(1000\) three.
- Move every digit that many places to the right.
- Fill any empty place with a zero, including a zero before the point.
The \(5\) ones become \(5\) tenths.
| \(5 \div 10\) | \(=\) | \(0.5\) |
Move every digit two places right.
| \(23 \div 100\) | \(=\) | \(0.23\) |
The \(6\) ones become \(6\) thousandths.
| \(6 \div 1000\) | \(=\) | \(0.006\) |
There are 100 cm in 1 m.
| \(250 \div 100\) | \(=\) | \(2.5\text{ m}\) |
Common pitfalls
Frequently asked questions
What happens when you divide a decimal by 10?
Every digit moves one place to the right, taking a place value ten times smaller. \(5 \div 10 = 0.5\).
Does the decimal point move?
No. The point stays where it is; the digits move to smaller places.
How many places for 1000?
Three places to the right, because \(1000\) has three zeros. \(6 \div 1000 = 0.006\).
Why is 8 divided by 100 written 0.08?
The \(8\) moves two places right into the hundredths, and a zero holds the empty tenths place.