Multiply by 10,100,1000
Theory
Multiplying by 10, 100 or 1000 makes a number ten, a hundred or a thousand times bigger, so every digit moves one, two or three places to the left. The decimal point stays still and zeros fill any empty places. This Year 5 maths page shows how this works for whole numbers and decimals, and how to multiply by multiples of ten such as \(30\) or \(400\).
Each place is worth ten times the place on its right. Multiplying by \(10\) moves every digit one place left; by \(100\), two places; by \(1000\), three places.
The decimal point does not move. The digits move past it, and empty places up to the ones are filled with zeros as placeholders: \(58 \times 100 = 5800\).
Decimals work the same way on a place value chart: every digit moves left past the decimal point. \(3.4 \times 10 = 34\) and \(0.03 \times 100 = 3\). Zeros in front of a whole number (like \(03\)) are not written.
To multiply by a multiple of ten, such as \(30\), multiply by \(3\) and then by \(10\): \(14 \times 30 = 14 \times 3 \times 10 = 420\).
How far the digits move:
| Multiply by | Digits move | Example |
|---|---|---|
| \(10\) | 1 place left | \(3.4 \times 10 = 34\) |
| \(100\) | 2 places left | \(5.8 \times 100 = 580\) |
| \(1000\) | 3 places left | \(9 \times 1000 = 9000\) |
How to multiply by 10, 100 or 1000
- Count the zeros: \(10\) has one, \(100\) two, \(1000\) three.
- Move every digit that many places to the left. The decimal point stays.
- Fill empty places up to the ones with zeros.
How to multiply by a multiple of ten
- Split the multiplier: \(30 = 3 \times 10\), \(400 = 4 \times 100\).
- Multiply by the single digit first.
- Then multiply by \(10\), \(100\) or \(1000\).
(i) \(58 \times 10\)
(ii) \(58 \times 100\)
(iii) \(9 \times 1000\)
| \(58 \times 10\) | \(=\) | \(580\) |
| \(58 \times 100\) | \(=\) | \(5800\) |
| \(9 \times 1000\) | \(=\) | \(9000\) |
(i) \(580\).
(ii) \(5800\).
(iii) \(9000\).
| \(3.4 \times 10\) | \(=\) | \(34\) |
The \(3\) moves to the tens and the \(4\) to the ones: \(34\).
| \(0.03 \times 100\) | \(=\) | \(3\) |
| \(5.8 \times 100\) | \(=\) | \(580\) |
Each digit moves two places left. A zero fills the ones in \(580\).
| \(2.75 \times 1000\) | \(=\) | \(2750\) |
Three places left: \(2750\).
(i) \(14 \times 30\)
(ii) \(0.7 \times 300\)
| \(14 \times 3\) | \(=\) | \(42\) |
| \(42 \times 10\) | \(=\) | \(420\) |
| \(0.7 \times 3\) | \(=\) | \(2.1\) |
| \(2.1 \times 100\) | \(=\) | \(210\) |
(i) \(420\).
(ii) \(210\).
(i) \(10\) pens
(ii) \(100\) pens
(iii) \(1000\) pens.
| \(3.20 \times 10\) | \(=\) | \(32\) |
| \(3.20 \times 100\) | \(=\) | \(320\) |
| \(3.20 \times 1000\) | \(=\) | \(3200\) |
(i) \(\$32\).
(ii) \(\$320\).
(iii) \(\$3200\).
| \(6.4 \to 640\) | \(:\) | \(\text{2 places left}\) |
The digits moved two places, so the box is \(100\).
Common pitfalls
Frequently asked questions
How do you multiply by 10?
Move every digit one place to the left. \(58 \times 10 = 580\) and \(3.4 \times 10 = 34\).
How do you multiply a decimal by 100?
Move every digit two places to the left. \(5.8 \times 100 = 580\).
Why do the digits move to the left?
Each place is worth ten times the place on its right. Multiplying by 10 makes every digit worth ten times as much, so each one moves into the next place to the left.
Why is “just add a zero” wrong?
It only works for whole numbers. For \(4.6\), adding a zero gives \(4.60\), which is the same number. The digits must move: \(4.6 \times 10 = 46\).
How do you multiply by 30 or 400?
Multiply by the digit first, then by \(10\) or \(100\). \(14 \times 30 = 42 \times 10 = 420\).