Multiply by 10, 100, 1000, and so on.

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Multiplying numbers by 10, 100, 1000, and so on (powers of 10) is a fundamental concept in mathematics. This process is relatively straightforward once you understand how place value works in our decimal number system. Let’s go through the process with some examples:

Basic Concept:

  1. Place Value Understanding: In our number system, each digit in a number has a place value, depending on its position. Moving a digit one place to the left increases its value tenfold.
  2. Multiplying by Powers of 10: When you multiply a number by 10, 100, 1000, etc., you’re essentially shifting each digit in the number to the left by one, two, three, etc., places, respectively. For each shift, a zero is added to the right of the number.

Steps for Multiplying by 10, 100, 1000:

  1. Multiply by 10: Move each digit in the number one place to the left and add one zero at the end.
    • Example: 35×10
      • Shift 35 one place left: 350.
  2. Multiply by 100: Move each digit in the number two places to the left and add two zeros at the end.
    • Example: 46×100
      • Shift 46 two places left: 4600.
  3. Multiply by 1000: Move each digit in the number three places to the left and add three zeros at the end.
    • Example: 29×1000
      • Shift 29 three places left: 29000.

Additional Examples:

  1. Multiplying a Two-Digit Number by 10
    • 72×10=720
    • Each digit in 72 moves one place to the left, adding a zero at the end.
  2. Multiplying a Three-Digit Number by 100
    • 123×100=12300
    • Each digit in 123 moves two places to the left, adding two zeros at the end.
  3. Multiplying a Four-Digit Number by 1000
    • 4567×1000=4567000
    • Each digit in 4567 moves three places to the left, adding three zeros at the end.

Tips:

  • Remember the Zeros: The number of zeros in the multiplier (10, 100, 1000, etc.) is the number of places you move each digit to the left in the original number.
  • No Calculation Needed: Unlike other multiplication, you don’t need to calculate – just shift digits and add zeros.
  • Decimal Numbers: The same rule applies. For example, 2.5×100=250. The decimal point moves two places to the right.

Conclusion

Multiplying by 10, 100, 1000, and other powers of 10 is a matter of understanding place value and shifting digits. This concept is crucial in mathematics as it simplifies calculations and helps in understanding more complex concepts related to place value and number manipulation. Remember, each zero in the multiplier adds a new place to the number being multiplied, shifting all its digits to the left.

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