1/9+2/9=3/9=0.111...+0.222...=0.333...Similarly 2/9+3/9=0.555....
This come to the results, such as 2/9+7/9=0.222...+0.777..=0.999...But 2/9+7/9=9/9,
Then9/9=1=0.999... Why this happen?
2006-12-31 20:23:17 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
0.9999 repeating is equal to 1
2007-01-04 19:19:01 · answer #1 · answered by Anonymous · 0⤊ 0⤋
9/9=1, not .99. 9 divided by 9=1.
1/9+2/9+3/9=6/9=. 2/3=.67(rounded to the nearest hundredth)
2/9+3/9= 5/9=.555
2/9+7/9=9/9=1 How did you get .222? Divide 9 into 9
9/9=1, not .999, but .999 rounded to the nearest unit is 1
.111+.222+.333=.666=2/3
The difference is because none o the fractions come out even when converted to decimals.The difference is negligible.
2006-12-31 21:35:33 · answer #2 · answered by Max 6 · 0⤊ 0⤋
A calculator only shows as much of the answer as its screen is wide. 1/9 has an infinite number of "1's" after the decimal point. And yes, 0.999 repeating an infinite number of times is the same as 1.
2006-12-31 20:30:03 · answer #3 · answered by Regala 1 · 2⤊ 0⤋
The reason is .99999 ... ( n digits) = 1 - (1/10)^n
when n = 1 it is .9 or 1 - .1
n =2 it is .99 or 1-.01 = 1-(1/10)^2
when n->infinite as this has infinite digits limit is 1
2006-12-31 20:45:59 · answer #4 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
The reason is because 0.9999(repeating forever) IS equal to 1, despite the many people who don't believe it.
0.999(repeating) represents an infinite series which is equal to 1. Nothing to do with rounding.
Many nonmath-minded people refuse to believe they are equal, but it's because the concept of infinity is tied to it.
2006-12-31 20:30:00 · answer #5 · answered by Puggy 7 · 2⤊ 1⤋
1/9 = 0.11111111. . .
2/9 = .222222222. . .
3/9= .333333333.. .
8/9 = .88888888. . . .
This is a repeating decijal and goes on to infinity ( ∞ )
- - - - -s-
2006-12-31 23:53:02 · answer #6 · answered by SAMUEL D 7 · 0⤊ 0⤋
Let say we don't know what is number of 9/9!
But, we know
1/9=0.11...
Then, we can write like that
1=9*0.11...
9/9
= (1+1+1+1+1+1+1+1+1)/9
= 1/9+1/9+1/9+1/9
+1/9+1/9+1/9+1/9+1/9
= 0.11..+0.11..+0.11..+0.11..
+0.11..+0.11..+0.11..+0.11..
+0.11..
=9*0.11..
=1
2006-12-31 21:28:37 · answer #7 · answered by seah 7 · 0⤊ 0⤋
take 0.99=x;
multiply by 10 on both sides
9.9=10x;
9+x=10x
9=9x;
x=1;
voila! 0.99=1
2007-01-01 00:24:40 · answer #8 · answered by IN PURSUIT OF WISDOM 2 · 0⤊ 0⤋