A page from a story book has a thickness of 2.5•10-² centimeter and a page from a dictionary has a thickness of 5•10-³ centimeter. which book has a thicker page? how much thicker is the page?
Accepted Solution
A:
Answer:A page from a story book is thicker. It is thicker by [tex]2\times 10^{-2}\textrm{ cm}[/tex].Step-by-step explanation:Given:Thickness of a page from story book = [tex]2.5\times 10^{-2}\textrm{ cm}[/tex]Thickness of a page from a dictionary = [tex]5\times 10^{-3}\textrm{ cm}[/tex]Now, in order to compare the thickness of both the pages, we have to rewrite their measurements in same exponents of 10.Exponent of 10 for story book is -2 and exponent of 10 for dictionary is -3.Let us rewrite the measurement of page from dictionary.[tex]5\times 10^{-3}=5\times 10^{-2-1}=5\times 10^{-2}\times 10^{-1}=5\times 10^{-2}\times \frac{1}{10}=\frac{5}{10}\times 10^{-2}=0.5\times 10^{-2}\textrm{ cm}[/tex]Now, thickness of a page from dictionary is [tex]0.5\times 10^{-2}\textrm{ cm}[/tex] while thickness from story book's page is [tex]2.5\times 10^{-2}\textrm{ cm}[/tex]. Clearly, a page from story book is thicker as 2.5 is greater than 0.5.Now, difference in thickness is:[tex]=(2.5\times 10^{-2})-(0.5\times 10^{-2})\\=(2.5-0.5)\times 10^{-2}=2.0\times 10^{-2}\textrm{ cm}[/tex]Therefore, a page from story book is thicker than a page from dictionary by a difference of [tex]2\times 10^{-2}\textrm{ cm}[/tex].