When multiplying a decimal by a power of 10, the product

Answer 1

When multiplying a decimal by a power of 10, the product is obtained by moving the decimal point to the right for positive powers of 10 or to the left for negative powers of 10.

• For positive powers of 10 (e.g., 10^1, 10^2, etc.), the decimal point moves to the right:

  • Example: $2.5\times {10}^2=2.5\times 100=250$ (the decimal point moves 2 places to the right)

• For negative powers of 10 (e.g., 10^-1, 10^-2, etc.), the decimal point moves to the left:

  • Example: $2.5\times {10}^{-2}=2.5\times 0.01=0.025$ (the decimal point moves 2 places to the left)

This allows for a simple way to scale decimal numbers up or down by factors of ten.