Question

The diameter of a pearl is about 4 x 10-3cm and the diameter of an atom is about10-11m. How much larger than an atom is a pearl?Show your work.

a)14x 10∧-14times b) 4 x 10 ∧-14timesc) 14x 10∧-11times d) 4 x 10∧6times

Answer 1

d)
`4\cdot 10^(6)` times

Explanation:

Scientific Notation

We are given two quantities and we must find the ratio between them and use scientific notation.

The diameter of a pearl is about

`4\cdot 10^(-3)\ cm`

Converting to meters, we divide by 100

`4\cdot 10^(-3) / 100 = 4\cdot 10^(-5)\ m`

The diameter of an atom is about

`10^(-11)\ m`

The ratio between both diameters is:

`\displaystyle (4\cdot 10^(-5)\ m)/(10^(-11)\ m)= 4\cdot 10^(-5+11)=4\cdot 10^(6)`

Answer: d)
`\mathbf{4\cdot 10^(6)}` times