Skill: Identify multiplication patterns

When a factor is multiplied by $10$, $100$, or $1{,}000$, the value of every digit shifts to a larger place-value position.

• Multiplying by $10$ shifts each digit 1 place left.
• Multiplying by $100$ shifts each digit 2 places left.
• Multiplying by $1{,}000$ shifts each digit 3 places left.

This changes the value of the digits; it is not just “adding zeros.”

Worked example

Complete the pattern:

$$4.27 \times 1,\quad 4.27 \times 10,\quad 4.27 \times 100,\quad 4.27 \times 1{,}000$$

Start with $4.27$.

1. Multiplying by $1$ does not change the number:

$$4.27 \times 1 = 4.27$$

2. Multiplying by $10$ shifts each digit 1 place left:

$$4.27 \times 10 = 42.7$$

3. Multiplying by $100$ shifts each digit 2 places left:

$$4.27 \times 100 = 427$$

4. Multiplying by $1{,}000$ shifts each digit 3 places left:

$$4.27 \times 1{,}000 = 4{,}270$$

The completed pattern is:

$$4.27,\quad 42.7,\quad 427,\quad 4{,}270$$

Notice that each time the number is multiplied by another factor of $10$, every digit becomes worth 10 times as much. Also, multiplying by $0$ always gives $0$:

$$4.27 \times 0 = 0$$