Question

Math question

Answer 1

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 $3.0 * 10^5$