Why Does Multiplying by 10, 100, or 1,000 Add Zeros?

📚 Understanding Place Value

The key to understanding why multiplying by 10, 100, or 1000 adds zeros lies in the concept of place value. Our number system is based on powers of 10, where each digit's position determines its value.

• 📍 Ones Place: The rightmost digit represents the number of ones.
• 💯 Tens Place: The digit to the left of the ones place represents the number of tens.
• 🏘️ Hundreds Place: The next digit represents the number of hundreds, and so on.

➕ Multiplication as Repeated Addition

Multiplication can be thought of as repeated addition. For example, $3 \times 10$ is the same as adding 10 three times: $10 + 10 + 10 = 30$.

🔢 Multiplying by 10

When you multiply a number by 10, you're essentially shifting all the digits one place to the left. This is because each digit's value becomes ten times greater. To hold the place, a zero is added to the end.

• ➡️ Example: $5 \times 10 = 50$. The 5 moves from the ones place to the tens place.
• ➕ This is the same as adding 5 to itself ten times.
• ✨ The added zero ensures the 5 now represents 5 tens.

💯 Multiplying by 100

Multiplying by 100 is like multiplying by 10 twice. Each digit shifts two places to the left, and two zeros are added as placeholders.

• ✔️ Example: $7 \times 100 = 700$. The 7 moves from the ones place to the hundreds place.
• ➕ Equivalent to adding 7 to itself one hundred times.
• ✨ Two zeros are added because the 7 now represents 7 hundreds.

🚀 Multiplying by 1,000

Similarly, multiplying by 1,000 shifts each digit three places to the left, adding three zeros.

• ✔️ Example: $2 \times 1000 = 2000$. The 2 moves from the ones place to the thousands place.
• ➕ Same as adding 2 to itself one thousand times.
• ✨ Three zeros are added because the 2 now represents 2 thousands.

➗ Division as the Inverse Operation

Division is the inverse of multiplication. When dividing by 10, 100, or 1000, you effectively remove zeros (or shift the decimal point to the left).

➗ Examples:

• ➗ $30 \div 10 = 3$ (Remove one zero)
• ➗ $500 \div 100 = 5$ (Remove two zeros)
• ➗ $8000 \div 1000 = 8$ (Remove three zeros)

📊 Table Summary