How can 0.99999... be converted into a proper fraction. Why is that the answer?
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We have to convert 0.99999..... into a proper fraction.
Let 0.99999... = f
10f = 9.9999...
10f - f = 9.99999... - 0.99999
=> 9f = 9
=> f = 9/9
=> f = 1/1
The representation of .9999... as a proper fraction is 1/1 because in 0.999... as the number of 9s in the decimal tends to infinity its value tends to 1. Here the number of 9s in the decimal part is tending to infinity; this makes 0.999... equal to 1.
The proper fraction representation of 0.999... is 1/1.
Related Questions
- Convert 57% into a decimal and fraction, reduce fraction to its lowest term
- 1 Educator Answer
- How to change 2.2 into a fraction
- 1 Educator Answer
- How do you change a fraction into a decimal? e.g 1/3=_.___
- 2 Educator Answers
- How do I convert fractions into decimals?
- 2 Educator Answers
- How do you convert fractions to decimals, and decimals to fractions?
- 1 Educator Answer
Let 0.99999... = p be the proper fraction.
p = 0.999..... (1).
Multiply both sides of equation at (1) by 10.
10p = 9.999.... (2)
(2) - (1):
10p - p = (9.999...) - (0.999.....)
9p = 9.
p = 9/9 = 1/1.
Therefore p = 1/1. Or p = 1.
Student Answers