Multiply & divide by 10, 100, 1000 - Divide by 10,100,1000
Theory
Dividing by \(10\), \(100\) or \(1000\) moves every digit to the right — one place for each zero. The digits move; the decimal point stays, and a leading zero holds an empty ones place.
Dividing by \(10\), \(100\) or \(1000\) makes a number smaller, so every digit moves to a lower place: to the right.
Count the zeros to see how far: \(\div 10\) moves \(1\) place, \(\div 100\) moves \(2\), \(\div 1000\) moves \(3\).
The digits move; the decimal point stays still.
A zero in front of the point holds an empty ones place, so \(4 \div 10 = 0.4\).
The number of zeros tells you how many places the digits move to the right.
| Divide by | Move | Example |
|---|---|---|
| \(\div 10\) | 1 place right | \(340 \rightarrow 34\) |
| \(\div 100\) | 2 places right | \(25 \rightarrow 0.25\) |
| \(\div 1000\) | 3 places right | \(1250 \rightarrow 1.25\) |
How to divide by 10, 100 or 1000
- Count the zeros. One for \(10\), two for \(100\), three for \(1000\).
- Move the digits right. Slide every digit that many places to the right.
- Hold the ones place. Write a zero in front of the point if the ones place is empty.
Move each digit one place right.
| \(340 \div 10\) | \(=\) | \(34\) |
The \(6\) moves to ones, the \(2\) to tenths.
| \(62 \div 10\) | \(=\) | \(6.2\) |
Move two places right; a leading zero holds the ones.
| \(25 \div 100\) | \(=\) | \(0.25\) |
One bead weighs \(1.25\) g.
| \(1250 \div 1000\) | \(=\) | \(1.25\) |
Common pitfalls
Frequently asked questions
What happens when you divide by 10?
Every digit moves one place to the right, so \(340 \div 10 = 34\) and \(62 \div 10 = 6.2\).
How do you divide by 100?
Move each digit two places right. For \(25 \div 100\), a leading zero holds the ones place, giving \(0.25\).
Why write a zero in front of the point?
To hold an empty ones place. \(4 \div 10 = 0.4\); the zero shows there are no whole ones.
Can you just cross off a zero to divide by 10?
Only for round numbers like \(340\). For \(62 \div 10\) the digits must move, giving \(6.2\).
Does the decimal point move when dividing?
No. The digits move to the right; the point stays where it is.