Multiplying and Dividing by Powers of 10

Our number system is based on Powers of 10, such as 1, 10, 100, 1000, 10,000, etc. This makes multiplication and division by these powers straightforward.

Multiplication by Powers of 10

• Concept: When multiplying any number by a power of 10, you essentially add zeros to the right of the number based on the number of zeros in the power of 10.

• Example with Single Digit:

  • Multiply 5 by 10 → 50
  • Multiply 5 by 100 → 500
  • Multiply 5 by 1000 → 5000

• Example with Multi-digit Number:

  • Multiply 293 by 1000: Add three zeros to make 293,000.

• Decimal Multiplication: Simply shift the decimal point to the right by the number of zeros.

  • Multiply 0.062 by 1000 results in 62, as the decimal point is shifted three places right.

Division by Powers of 10

• Concept: When dividing by a power of 10, shift the decimal point to the left by the number of zeros.
• Example with Whole Number:
  • Divide 800 by 10: Shift the decimal left by one place, resulting in 80.
• Example with Multi-digit Number:
  • Divide 410 by 10,000: Shift the decimal point four places left, resulting in 0.041.

Tips and Tricks

• Decimal Point Shifting: The decimal point is between the ones place and the tenths place. To multiply or divide, simply shift the point.
• Decimal Filling: If shifting moves the point beyond the digits, fill the empty spaces with zeros.
• Zero Trimming: Remove unnecessary starting zeros on the left and ending zeros on the right to simplify numbers.

Conclusion

Practice by multiplying and dividing numbers using powers of 10, shifting the decimal point right for multiplication and left for division. To enhance your skills, you can try practice problems and access printable worksheets at mathantics.com.