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hichkok12 [17]
2 years ago
9

Math question

Mathematics
1 answer:
AleksandrR [38]2 years ago
3 0

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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