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The ratio \[\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}\] is closest to which whole number?

 Jun 13, 2019
edited by sinclairdragon428  Jun 13, 2019
edited by sinclairdragon428  Jun 13, 2019

Best Answer 

 #1
avatar+8579 
+2

\(\ \phantom{=\quad}\dfrac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}\\~\\ =\quad\dfrac{10^{2000}(1+10^{2})}{10^{2000}(10+10)}\\~\\ =\quad\dfrac{(1+10^{2})}{(10+10)}\\~\\ =\quad\dfrac{(1+100)}{20}\\~\\ =\quad\dfrac{1}{20}+\dfrac{100}{20}\\~\\ =\quad\dfrac{1}{20}+5 \)

 

The whole number closest to  5  and  1/20th  is  5 .

 Jun 13, 2019
 #1
avatar+8579 
+2
Best Answer

\(\ \phantom{=\quad}\dfrac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}\\~\\ =\quad\dfrac{10^{2000}(1+10^{2})}{10^{2000}(10+10)}\\~\\ =\quad\dfrac{(1+10^{2})}{(10+10)}\\~\\ =\quad\dfrac{(1+100)}{20}\\~\\ =\quad\dfrac{1}{20}+\dfrac{100}{20}\\~\\ =\quad\dfrac{1}{20}+5 \)

 

The whole number closest to  5  and  1/20th  is  5 .

hectictar Jun 13, 2019
 #2
avatar+248 
+1

Thank you!

sinclairdragon428  Jun 13, 2019

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