document.write( "Question 199187: There is a question here which says '6e, where e=2.718...\r
\n" ); document.write( "\n" ); document.write( "How do you solve that and is it Rational or Irrational? \n" ); document.write( "

Algebra.Com's Answer #149655 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You cannot 'solve' it in any sense of the word solve that I know. The only way to express

exactly is just that:

. You can express a numerical approximation to as many decimal places as you like by multiplying 6 times an appropriately precise representation of

. The Windows built-in calculator gives e to more decimal places than I can conceive of a practical use, namely: 2.7182818284590452353602874713527. But if that is insufficient for your needs you can use the following:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The larger number you select for

, the closer you get. For example

gets you a nine-digit decimal approximation.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

is most assuredly irrational. In fact, it is transcendental, meaning that it is not an algebraic number, that is, it is not the root of any polynomial equation with rational coefficients.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "John
\n" ); document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );