Question

When you multiply a decimal by a power of ten,what is the relationship between the number of places the decimal point moves and the number of zeros in the power of ten

Answer 1

Answer:

  it depends

Step-by-step explanation:

For positive powers of 10, the decimal point moves right 1 place for each zero in the power of 10.

Example:

  1.2345 × 10³ = 1.2345 × 1000 = 1234.5 × 1 = 1234.5

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For negative powers of 10, the decimal point moves left 1 more place than there are zeros in the power of 10.

Example:

  1234.5 × 10⁻³ = 1234.5 × 0.001 = 1.2345

  there are 2 zeros in .001, but the decimal point moves 3 places, corresponding to the exponent of 3 in the power of 10.