Answer:
You'd be [tex]2 * 10^{-6}[/tex] times tall
Step-by-step explanation:
Given
Represent the previous and new diameter by D1 and D2;
[tex]D_1 = 2 * 10^{-8}m[/tex]
[tex]D_2 = 1\ cm[/tex]
To determine how tall you'd be, we need to divide D2 by D1;
[tex]Ratio = \frac{D_2}{D_1}[/tex]
Substitute values for D2 and D1
[tex]Ratio = \frac{2 * 10^{-8}m}{1\ cm}[/tex]
Convert cm to m
[tex]Ratio = \frac{2 * 10^{-8}m}{1 * 0.01\ m}[/tex]
[tex]Ratio = \frac{2 * 10^{-8}m}{0.01\ m}[/tex]
Convert denominator to exponents
[tex]Ratio = \frac{2 * 10^{-8}m}{10^{-2}\ m}[/tex]
[tex]Ratio = \frac{2 * 10^{-8}}{10^{-2}}[/tex]
Apply Law of indices
[tex]Ratio = 2 * 10^{-8} * 10^2[/tex]
[tex]Ratio = 2 * 10^{-8+2}[/tex]
[tex]Ratio = 2 * 10^{-6}[/tex]
Hence;
You'd be [tex]2 * 10^{-6}[/tex] times tall
