Multiply by 10 & 100
Theory
Multiplying by 10 and 100 is a Year 4 maths place value skill. To multiply by 10, every digit moves one place to the left; to multiply by 100, every digit moves two places to the left. This page shows the place value shift on a chart, explains why a zero holds each empty place, and warns against thinking of it as just adding a zero. Curriculum: VC2M4N05 / AC9M4N05.
To multiply a number is to make it a number of times as large. Multiplying by 10 makes a number ten times as large, and multiplying by 100 makes it one hundred times as large.
When you multiply by 10, every digit moves one place to the left. Ones become tens and tens become hundreds. The ones place is now empty, so a zero is written to hold it: \(6 \times 10 = 60\). This is called the place value shift.
When you multiply by 100, every digit moves two places to the left, so two zeros hold the empty tens and ones places: \(2 \times 100 = 200\). The zero is a placeholder — it is the shift, not the zero, that makes the number bigger.
Multiplying by 10 and 100 is not a new fact to memorise — it is a place value shift. These facts help you build and check your answers.
How to multiply by 10 or 100
- Choose the shift. Multiplying by 10 moves each digit one place left. Multiplying by 100 moves each digit two places left.
- Slide the digits. Move every digit into its new, bigger place: ones to tens, tens to hundreds, and so on.
- Hold the empty places. Write one zero for \(\times 10\) or two zeros for \(\times 100\), then read the new number.
| \(4\text{ tens}\) | \(\to\) | \(4\text{ hundreds}\) |
| \(8\text{ ones}\) | \(\to\) | \(8\text{ tens}\) |
| \(48 \times 10\) | \(=\) | \(480\) |
A zero holds the empty ones place, so the answer is \(480\).
| \(2\text{ tens}\) | \(\to\) | \(2\text{ thousands}\) |
| \(6\text{ ones}\) | \(\to\) | \(6\text{ hundreds}\) |
| \(26 \times 100\) | \(=\) | \(2600\) |
Two zeros hold the empty tens and ones places, so the answer is \(2600\).
| \(8\text{ bags of }100\) | \(=\) | \(8 \times 100\) |
| \(8\text{ ones}\) | \(\to\) | \(8\text{ hundreds}\) |
| \(8 \times 100\) | \(=\) | \(800\) |
There are \(800\) marbles.
| \(12 \times 10\) | \(=\) | \(120\) |
| \(120 \times 10\) | \(=\) | \(1200\) |
| \(12 \times 100\) | \(=\) | \(1200\) |
Two shifts of one place is the same as multiplying by \(100\).
Common pitfalls
Frequently asked questions
What happens when you multiply a number by 10?
The number becomes ten times as large, so every digit moves one place to the left. Ones become tens and tens become hundreds. A zero is written in the ones place to hold it, so \(6 \times 10 = 60\).
What is the rule for multiplying by 100?
Every digit moves two places to the left, because the number becomes one hundred times as large. Two zeros hold the empty tens and ones places, so \(2 \times 100 = 200\).
Why do you write a zero when you multiply by 10?
Because every digit moves one place to the left, the ones place is left empty. The zero is a placeholder that keeps the other digits in their new, larger places. It is the shift that makes the number bigger, not the zero.
Is multiplying by 10 the same as adding 10?
No. Multiplying by 10 makes a number ten times as large, so \(6 \times 10 = 60\). Adding 10 only makes it 10 more, so \(6 + 10 = 16\). They give very different answers.
How can you multiply by 100 using two steps?
Multiply by 10, then multiply that answer by 10 again. Each step shifts the digits one place left, so two steps shift them two places, which is the same as multiplying by 100. For example, \(12 \times 10 = 120\) and \(120 \times 10 = 1200\).
What is 40 times 10?
\(40\) has 4 tens. Each digit moves one place to the left, so the 4 tens become 4 hundreds and a zero holds the ones place. \(40 \times 10 = 400\).