Identify multiplication patterns

Multiplication patterns describe how products change when a factor changes in a regular way, including the effects of multiplying whole numbers and decimals by 10, 100, and 1,000, and the roles of factors such as 0 and 1. The learner interprets these patterns through place value, equations, tables, and multiples, understanding that multiplying by powers of ten shifts each digit’s value rather than merely “adding zeros”; formal algebraic generalization beyond these numerical cases is not included.

Detailed Explanation: 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 $4.27$ .

Multiplying by $1$ does not change the number:

4.27 \times 1 = 4.27

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

4.27 \times 10 = 42.7

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

4.27 \times 100 = 427

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

Learn by doing: Identify multiplication patterns

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Multiplication - Decimal Tenths by Hundreds

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