Question

9. The average diameter of an atom is 2 x 10-8 m. What if the average diameter of an atom was 1 cm? How tall would you be?

Answer 1

You'd be
`2 * 10^(-6)` times tall

Explanation:

Given

Represent the previous and new diameter by D1 and D2;

`D_1 = 2 * 10^(-8)m`

`D_2 = 1\ cm`

To determine how tall you'd be, we need to divide D2 by D1;

`Ratio = (D_2)/(D_1)`

Substitute values for D2 and D1

`Ratio = (2 * 10^(-8)m)/(1\ cm)`

Convert cm to m

`Ratio = (2 * 10^(-8)m)/(1 * 0.01\ m)`

`Ratio = (2 * 10^(-8)m)/(0.01\ m)`

Convert denominator to exponents

`Ratio = (2 * 10^(-8)m)/(10^(-2)\ m)`

`Ratio = (2 * 10^(-8))/(10^(-2))`

Apply Law of indices

`Ratio = 2 * 10^(-8) * 10^2`

`Ratio = 2 * 10^(-8+2)`

`Ratio = 2 * 10^(-6)`

Hence;

You'd be
`2 * 10^(-6)` times tall