As you know, 0.75=3/4 ; 0.5=1/2; 0.333...=1/3. Also more,
1/9=0.111...;2/9=0.222...;8/9=0.888...And 3/9+5/9=0.333...+0.555...=0.888...=8/9.Then 0.999...is made from what fraction?
2007-01-02 11:05:30 · 11 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
x=.9999999...........................................
10x=9.9999999999999999999999999....
9x=9
x=1
so for all practical purposes 0.9 recurring=1
2007-01-02 11:08:18 · answer #1 · answered by raj 7 · 0⤊ 1⤋
Since 0.999... is equal to 1 the fraction can be named by 9/9.
When we add the two fractions above together we get the third fraction.
1/9 = 0.111...
8/9 = 0.888...
9/9 = 0.999...
Have a great week!
EDs
2007-01-02 11:09:15 · answer #2 · answered by Eds 7 · 0⤊ 0⤋
I assume you mean that for 0.999... the 9 is understood to repeat forever.
In that case you could say it is 3/3 or 9/9 or any number of other fractions as well. However these two are the most straight forward. So
0.999... = 9/9 = 1
when the 9 repeats forever.
2007-01-02 11:10:36 · answer #3 · answered by Northstar 7 · 0⤊ 0⤋
1/9 = 0.1111...
2/9 = 0.2222...
3/9 = 0.3333... = 1/3
4/9 = 0.4444...
5/9 = 0.5555...
6/9 = 0.6666... = 2/3
7/9 = 0.7777...
8/9 = 0.8888...
9/9 = 0.9999... = 1
You can make it from any combination of fractions that add to 1, such as:
2/9 + 7/9 = 1
0.2222... + 0.7777... = 0.9999... = 1
or:
1/3 + 1/3 + 1/3 = 1
0.3333... + 0.3333... + 0.3333... = 0.9999... = 1
So you have just proven that 0.9999... is the same thing as 1.
2007-01-02 11:08:45 · answer #4 · answered by Puzzling 7 · 0⤊ 0⤋
The answer is 1.
let x = 0.999......
Therefore, 10x = 9.999............
9.999.........-0.999.........=9, and substituting we see that 10x - x also = 9. If 9x = 9, then x = 1. Since x also = 0.999......, it follows that0.999......... = 1.
2007-01-02 12:19:22 · answer #5 · answered by operalph 4 · 0⤊ 0⤋
The fraction is 1/1.001001001
2007-01-02 11:09:36 · answer #6 · answered by Joe K 6 · 0⤊ 2⤋
999/1000
2007-01-02 11:14:13 · answer #7 · answered by Anonymous · 0⤊ 2⤋
999/1000
2007-01-02 11:07:47 · answer #8 · answered by Flab 3 · 0⤊ 3⤋
999/1000
2007-01-02 11:07:27 · answer #9 · answered by Deuce 2 · 1⤊ 3⤋
Such a fraction does not exist.
2007-01-02 11:13:19 · answer #10 · answered by ironduke8159 7 · 0⤊ 2⤋