Question

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? ​

Answer 1

A page from a story book is thicker. It is thicker by
`2* 10^(-2)\textrm{ cm}`.

Explanation:

Given:

Thickness of a page from story book =
`2.5* 10^(-2)\textrm{ cm}`

Thickness of a page from a dictionary =
`5* 10^(-3)\textrm{ cm}`

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.

`5* 10^(-3)=5* 10^(-2-1)=5* 10^(-2)* 10^(-1)=5* 10^(-2)* (1)/(10)=(5)/(10)* 10^(-2)=0.5* 10^(-2)\textrm{ cm}`

Now, thickness of a page from dictionary is
`0.5* 10^(-2)\textrm{ cm}` while thickness from story book's page is
`2.5* 10^(-2)\textrm{ cm}`.

Clearly, a page from story book is thicker as 2.5 is greater than 0.5.

Now, difference in thickness is:

`=(2.5* 10^(-2))-(0.5* 10^(-2))\\=(2.5-0.5)* 10^(-2)=2.0* 10^(-2)\textrm{ cm}`

Therefore, a page from story book is thicker than a page from dictionary by a difference of
`2* 10^(-2)\textrm{ cm}`.