SOLUTION: How do you find an irrational number between two other numbers -ex: 0.142 and 0.143 Thank you , Ashley

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Question 482770: How do you find an irrational number between two other numbers -ex: 0.142 and 0.143 Thank you , Ashley
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'll write the numbers given as fractions:
+.142+=+142%2F1000+
+.143+=+143%2F1000+
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Multiply both sides by 10
+.142+=+1420%2F10000+
+.143+=+1430%2F10000+
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If I add +.0003+ to top and bottom
of +1420+%2F+10000+
+1423+%2F+10003+=+.1422573+. . .
is less than +.143+, and, since both
+1423+ and +10003+ are prime,
the result is irrational