Math question Shannon and Kristoph are dividing numbers written in scientific notation. Shannon’s expression: 4.2 x 10

Question

Math question

Shannon and Kristoph are dividing numbers written in scientific notation.

Shannon’s expression: 4.2 x 10^9 /1.4 x 10^4

Kristoph’s expression: 4.2 x 10^2 /1.4 x 10^-3

C) What is the value of their expressions written in standard form?

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Gianna 3 weeks 2021-09-09T08:53:12+00:00 1 Answer 0

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    2021-09-09T08:54:19+00:00

    Answer:

    – Shannon’s expression in scientific notation is 3.0 * 10^5

    – Kristoph’s expression in scientific notation is 3.0 * 10^5

    Step-by-step explanation:

    Given

    Shannon’s expression: 4.2 * 10^9 /1.4 * 10^4

    Kristoph’s expression: 4.2 * 10^2 /1.4 * 10^{-3}


    Required

    What is the value of their expressions written in standard form

    First, we solve Shannon’s expression:

    4.2 * 10^9 /1.4 * 10^4

    Writing the expression properly

    \frac{4.2 * 10^9}{1.4 * 10^4}

    Split into two

    \frac{4.2}{1.4} * \frac{10^9}{10^4}

    3.0 * \frac{10^9}{10^4}

    From laws of indices \frac{a^m}{a^n} = a^{m-n}

    Applying the above law, we have

    3.0 * 10^{9-4}

    3.0 * 10^5

    Hence, Shannon’s expression in scientific notation is 3.0 * 10^5

    Applying the same steps on Kristoph’s expression; we have

    4.2 * 10^2 /1.4 * 10^{-3}

    Writing the expression properly

    \frac{4.2 * 10^2}{1.4 * 10^{-3}}

    Split into two

    \frac{4.2}{1.4} * \frac{10^2}{10^{-3}}

    3.0 * \frac{10^2}{10^{-3}}

    From laws of indices \frac{a^m}{a^n} = a^{m-n}

    Applying the above law, we have

    3.0 * 10^{2-(-3)}

    3.0 * 10^{2+3}

    3.0 * 10^5

    Hence, Kristoph’s expression in scientific notation is 3.0 * 10^5

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