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Rewrite the first number with the same exponent as the second number.

Mathematics

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Answer

−7.97×10−3-7.97 \times 10^{-3}

Step-by-step solution

3 steps
  1. Rewrite the first number with the same exponent as the second number.

    To subtract numbers in scientific notation, their exponents must be the same. We will convert 3×10−53 \times 10^{-5} to have an exponent of −3-3.

    3×10−5=3×10−2×10−3=0.03×10−33 \times 10^{-5} = 3 \times 10^{-2} \times 10^{-3} = 0.03 \times 10^{-3}
  2. Perform the subtraction.

    Now that both numbers have the same exponent (10−310^{-3}), we can subtract their coefficients.

    (0.03×10−3)−(8×10−3)=(0.03−8)×10−3(0.03 \times 10^{-3}) - (8 \times 10^{-3}) = (0.03 - 8) \times 10^{-3} 0.03−8=−7.970.03 - 8 = -7.97

    So the expression becomes:

    −7.97×10−3-7.97 \times 10^{-3}
  3. Ensure the result is in standard scientific notation.

    A number is in standard scientific notation when it is written as a×10ba \times 10^b, where 1≤∣a∣<101 \le |a| < 10 and bb is an integer. In our result, −7.97-7.97 satisfies 1≤∣−7.97∣<101 \le |-7.97| < 10.

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