Multiply decimals by 10, 100 and 1000

Multiplying decimals by 10, 100, and 1000 is straightforward once we understand the pattern. Here’s how it works, along with examples to make it clear.

Basic Concept:

When we multiply a decimal by 10, 100, or 1000, we move the decimal point to the right. The number of places we move the decimal depends on how many zeros are in the multiplier:

• Multiply by 10: Move the decimal point 1 place to the right.
• Multiply by 100: Move the decimal point 2 places to the right.
• Multiply by 1000: Move the decimal point 3 places to the right.

Examples:

1. Multiplying by 10:
   • Example 1: Multiply 3.45×10
     • Move the decimal 1 place to the right.
     • 3.45 becomes 34.5
     • Answer: 3.45×10=34.5
   • Example 2: Multiply 0.67×10
     • Move the decimal 1 place to the right.
     • 0.67 becomes 6.7
     • Answer: 0.67×10=6.7
2. Multiplying by 100:
   • Example 1: Multiply 2.35×100
     • Move the decimal 2 places to the right.
     • 2.35 becomes 235
     • Answer: 2.35×100=235
   • Example 2: Multiply 0.89×100
     • Move the decimal 2 places to the right.
     • 0.89 becomes 89
     • Answer: 0.89×100=89
3. Multiplying by 1000:
   • Example 1: Multiply 1.234×1000
     • Move the decimal 3 places to the right.
     • 1.234 becomes 1234
     • Answer: 1.234×1000=1234
   • Example 2: Multiply 0.056×1000
     • Move the decimal 3 places to the right.
     • 0.056 becomes 56
     • Answer: 0.056×1000=56

What if There Aren’t Enough Digits?

If the decimal doesn’t have enough digits to move the decimal point the required number of places, we simply add zeros at the end.

• Example: Multiply 4.5×100
  • Move the decimal 2 places to the right.
  • 4.5 becomes 450 (adding a zero to move the decimal)
  • Answer: 4.5×100=450

Visual Representation:

For a clearer understanding, here’s how we can visualize it:

• 3.45×10=34.5
  (Imagine moving the decimal from between 3 and 4 to between 4 and 5)
• 0.056×1000=56
  (Move the decimal from between 0 and 5 to after 6, resulting in 56)

These steps can be used to multiply any decimal by 10, 100, or 1000.