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Convert the following to the specified form: 4 rac12 kg to an improper fraction, the reciprocal of rac56, and 2.5 imes 103 J to ordinary form.

Mathematics

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Here are the solutions to the problems:

:
To express 4124\frac{1}{2} kg as an improper fraction, we multiply the whole number by the denominator and add the numerator. This sum becomes the new numerator, while the denominator remains the same.

  1. Multiply the whole number by the denominator.

    4×2=84 \times 2 = 8
  2. Add the numerator to the result from Step 1.

    8+1=98 + 1 = 9
  3. Place this sum over the original denominator.

    92\frac{9}{2}

    The improper fraction is 92 kg\boxed{\frac{9}{2} \text{ kg}}.

    :
    To find the reciprocal of a fraction, we simply invert the fraction (swap the numerator and the denominator).

  4. Identify the given fraction.

    56\frac{5}{6}
  5. Invert the fraction to find its reciprocal.

    Reciprocal of 56=65\text{Reciprocal of } \frac{5}{6} = \frac{6}{5}

    The reciprocal is 65\boxed{\frac{6}{5}}.

    :
    To write 2.5×1032.5 \times 10^3 J in ordinary form, we move the decimal point to the right by the number of places indicated by the exponent of 10.

  6. Identify the number and the exponent.

    2.5×1032.5 \times 10^3

    The exponent is 3, so we move the decimal point 3 places to the right.

  7. Move the decimal point.

    2.5→25002.5 \to 2500

    The ordinary form is 2500 J\boxed{2500 \text{ J}}.

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