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

Answer:

d) $4\cdot 10^{6}$ times

Step-by-step 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:

$\displaystyle \frac{4\cdot 10^{-5}\ m}{10^{-11}\ m}= 4\cdot 10^{-5+11}=4\cdot 10^{6}$

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