Why the decrease in one in the power of the final answer

Physics

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Answer

The decrease in the power of the final answer is due to converting the coefficient to standard scientific notation.

Step-by-step solution

4 steps
  1. Recall the calculated force before final adjustment.

    We calculated the force as:

    F=64×10−14 NF = 64 \times 10^{-14} \text{ N}
  2. Convert the coefficient to a value between 1 and 10.

    To express 64 as a number between 1 and 10, we divide it by 10:

    64=6.4×10164 = 6.4 \times 10^1
  3. Substitute this back into the expression for FF.

    F=(6.4×101)×10−14 NF = (6.4 \times 10^1) \times 10^{-14} \text{ N}
  4. Combine the powers of 10.

    When multiplying powers with the same base, you add the exponents:

    F=6.4×10(1+(−14)) NF = 6.4 \times 10^{(1 + (-14))} \text{ N} F=6.4×10−13 NF = 6.4 \times 10^{-13} \text{ N}

    The power decreased from −14-14 to −13-13 because we increased the coefficient from 64 to 6.4 (divided by 10), so we had to compensate by multiplying by 10110^1, which effectively added 1 to the exponent.

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