Divide by 10,100,1000
Theory
Dividing by 10, 100 or 1000 makes a number ten, a hundred or a thousand times smaller, so every digit moves one, two or three places to the right. Digits can move past the decimal point into the tenths and hundredths. This Year 5 maths page shows how this works, how to divide by multiples of ten, and how division undoes multiplication.
Dividing by \(10\) moves every digit one place to the right; by \(100\), two places; by \(1000\), three places. The decimal point stays still.
On a place value chart, digits can slide past the decimal point into the tenths and hundredths: \(63 \div 10 = 6.3\) and \(35 \div 100 = 0.35\). A zero is written in the ones place when there are no ones: \(8 \div 10 = 0.8\).
Division by \(10\), \(100\) or \(1000\) undoes multiplication by the same number: \(4.8 \times 100 = 480\), so \(480 \div 100 = 4.8\).
To divide by a multiple of ten such as \(20\), divide by \(10\) and then by \(2\): \(840 \div 20 = 84 \div 2 = 42\).
How far the digits move:
| Divide by | Digits move | Example |
|---|---|---|
| \(10\) | 1 place right | \(63 \div 10 = 6.3\) |
| \(100\) | 2 places right | \(35 \div 100 = 0.35\) |
| \(1000\) | 3 places right | \(9000 \div 1000 = 9\) |
How to divide by 10, 100 or 1000
- Count the zeros in \(10\), \(100\) or \(1000\).
- Move every digit that many places to the right. The decimal point stays.
- Write a zero in the ones place if it is empty, and drop zeros at the end of a decimal.
How to divide by a multiple of ten
- Split the divisor: \(20 = 10 \times 2\), \(300 = 100 \times 3\).
- Divide by \(10\) or \(100\), then by the single digit.
(i) \(580 \div 10\)
(ii) \(7300 \div 100\)
(iii) \(9000 \div 1000\)
| \(580 \div 10\) | \(=\) | \(58\) |
| \(7300 \div 100\) | \(=\) | \(73\) |
| \(9000 \div 1000\) | \(=\) | \(9\) |
(i) \(58\).
(ii) \(73\).
(iii) \(9\).
| \(63 \div 10\) | \(=\) | \(6.3\) |
| \(8 \div 10\) | \(=\) | \(0.8\) |
There are no ones in \(0.8\), so a zero holds the ones place.
| \(35 \div 100\) | \(=\) | \(0.35\) |
The \(3\) moves to the tenths and the \(5\) to the hundredths: \(0.35\).
| \(2750 \div 1000\) | \(=\) | \(2.75\) |
\(2.75\). The zero at the end, \(2.750\), is not needed.
(i) \(840 \div 20\)
(ii) \(450 \div 300\)
| \(840 \div 10\) | \(=\) | \(84\) |
| \(84 \div 2\) | \(=\) | \(42\) |
| \(450 \div 100\) | \(=\) | \(4.5\) |
| \(4.5 \div 3\) | \(=\) | \(1.5\) |
(i) \(42\).
(ii) \(1.5\).
(i) \(10\) people
(ii) \(100\) people
(iii) \(1000\) people?
| \(250 \div 10\) | \(=\) | \(25\) |
| \(250 \div 100\) | \(=\) | \(2.5\) |
| \(250 \div 1000\) | \(=\) | \(0.25\) |
(i) \(\$25\).
(ii) \(\$2.50\).
(iii) \(\$0.25\) (25 cents).
| \(507 \div 10\) | \(=\) | \(50.7\) |
The zero in \(507\) holds the tens place and cannot be crossed off. Every digit moves one place right: \(50.7\).
Common pitfalls
Frequently asked questions
How do you divide by 10?
Move every digit one place to the right. \(580 \div 10 = 58\) and \(63 \div 10 = 6.3\).
Why do the digits move to the right?
Each place is worth one tenth of the place on its left. Dividing by 10 makes every digit worth a tenth as much, so each one moves into the next place to the right.
What is 35 divided by 100?
Each digit moves two places right, so \(35 \div 100 = 0.35\).
Why can you not just cross off a zero?
Only zeros at the end of a whole number can be dropped that way. In \(507\) the zero is a placeholder, so \(507 \div 10 = 50.7\).
How do you divide by 20?
Divide by \(10\), then by \(2\). \(840 \div 20 = 84 \div 2 = 42\).