SOLUTION: Show that 0.00315 (line over 15) is a rational number by writing it as a fraction of integers

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Show that 0.00315 (line over 15) is a rational number by writing it as a fraction of integers      Log On


   

Question 75321This question is from textbook Alegbra 2 An Incremental Development
: Show that 0.00315 (line over 15) is a rational number by writing it as a fraction of integers This question is from textbook Alegbra 2 An Incremental Development

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Convert 0.0031515... to its fractional equivalent.
1) n = 0.0031515... Multiply by 1,000.
2) 1,000n = 3.1515... Multiply this by 100.
3) 100,000n = 315.1515... Subtract equation 2) from equation 3)
4) 100,000n - 1,000n = 99,000n = 315.1515-3.1515 = 312
5) 99,000n = 312 Divide both sides by 99,000
6) n+=+312%2F99000 but, from equation 1) n = 0.0031515..., so:
7) 0.0031515+=+312%2F99000 Check this out in your calculator.