document.write( "Question 482770: How do you find an irrational number between two other numbers -ex: 0.142 and 0.143 Thank you , Ashley \n" ); document.write( "

Algebra.Com's Answer #330423 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll write the numbers given as fractions:
\n" ); document.write( " $\"+.142+=+142%2F1000+\"$
\n" ); document.write( " $\"+.143+=+143%2F1000+\"$
\n" ); document.write( "------------------
\n" ); document.write( "Multiply both sides by $\"10\"$
\n" ); document.write( " $\"+.142+=+1420%2F10000+\"$
\n" ); document.write( " $\"+.143+=+1430%2F10000+\"$
\n" ); document.write( "------------------
\n" ); document.write( "If I add $\"+.0003+\"$ to top and bottom
\n" ); document.write( "of $\"+1420+%2F+10000+\"$
\n" ); document.write( " $\"+1423+%2F+10003+=+.1422573+\"$ . . .
\n" ); document.write( "is less than $\"+.143+\"$ , and, since both
\n" ); document.write( " $\"+1423+\"$ and $\"+10003+\"$ are prime,
\n" ); document.write( "the result is irrational \n" ); document.write( "

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