SOLUTION: please help Show that 3.6123 (line over 123) is a rational number by writing it as a fraction of integers.

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Question 75312This question is from textbook Alegbra 2 An Incremental Development
: please help
Show that 3.6123 (line over 123) 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 3.6123123... to its fractional equivalent.
Let:
1) n = 3.6123123... Multiply this by 10.
2) 10n = 36.123123... Multiply again by 1,000
3) 10,000n = 36123.123123... Now subtract equation 2) from equation 3)
4) 10,000n-10n = 9990n = 36087 Now divide by 9990
5) n+=+36087%2F9990 but equation 1) shows: n = 3.6123123..., therefore, we have:
3.6123123+=+36087%2F9990
Check this out with your calculator.
I'm sorry but I don't know how to show the overscore above the repeated part of the decimal.