Answer:
- Shannon's expression in scientific notation is [tex]3.0 * 10^5[/tex]
- Kristoph's expression in scientific notation is [tex]3.0 * 10^5[/tex]
Step-by-step explanation:
Given
Shannon’s expression: [tex]4.2 * 10^9 /1.4 * 10^4[/tex]
Kristoph’s expression: [tex]4.2 * 10^2 /1.4 * 10^{-3}[/tex]
Required
What is the value of their expressions written in standard form
First, we solve Shannon's expression:
[tex]4.2 * 10^9 /1.4 * 10^4[/tex]
Writing the expression properly
[tex]\frac{4.2 * 10^9}{1.4 * 10^4}[/tex]
Split into two
[tex]\frac{4.2}{1.4} * \frac{10^9}{10^4}[/tex]
[tex]3.0 * \frac{10^9}{10^4}[/tex]
From laws of indices [tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
Applying the above law, we have
[tex]3.0 * 10^{9-4}[/tex]
[tex]3.0 * 10^5[/tex]
Hence, Shannon's expression in scientific notation is [tex]3.0 * 10^5[/tex]
Applying the same steps on Kristoph's expression; we have
[tex]4.2 * 10^2 /1.4 * 10^{-3}[/tex]
Writing the expression properly
[tex]\frac{4.2 * 10^2}{1.4 * 10^{-3}}[/tex]
Split into two
[tex]\frac{4.2}{1.4} * \frac{10^2}{10^{-3}}[/tex]
[tex]3.0 * \frac{10^2}{10^{-3}}[/tex]
From laws of indices [tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
Applying the above law, we have
[tex]3.0 * 10^{2-(-3)}[/tex]
[tex]3.0 * 10^{2+3}[/tex]
[tex]3.0 * 10^5[/tex]
Hence, Kristoph's expression in scientific notation is [tex]3.0 * 10^5[/tex]
