Is it really equal to 1
try
1-0.999999999999999..........
2006-11-14 18:52:08 · 10 answers · asked by behroz_ahmedali 2 in Science & Mathematics ➔ Mathematics
let x = 0.9999....
10x = 9.99999...
10x- x = 9.9999... - 0.99999....
9x = 9
x = 1 = 0.99999.....
2006-11-14 18:55:07 · answer #1 · answered by Demiurge42 7 · 3⤊ 0⤋
Hey! .9999 recurring IS equal to 1! This is how it works:
Surely you know that 1/3 can be written decimally as 0.333 recurring. Note that by multiplying a third by three, we get three thirds (3/3) , which is equal to one.
If we look at this same process decimally, take the number 0.33333 recurring and multiply it by 3, and you will see that each 3 in the sequence converts to a 9. This gives us .999 recurring, which, since it is the same as 3/3, is also equal to 1, as explained in the previous paragraph.
The reason for this is that as you add more 9s onto the number 0.9 (after the decimal point), it gets closer and closer to 1. Since there are an infinite number of 9s after the point in 0.99999 recurring, the difference between this number and 1 must be infinitely small, and therefore cannot be any greater than 0.
Hope that helps!
2006-11-14 19:02:14 · answer #2 · answered by thesekeys 3 · 1⤊ 0⤋
First consider 1/3 =0.333..
multiply both sides by 3
we get 1/3 x 3 = 1 on the left side, and on the right side we would have 0.33333... x 3 = 0.9999..
It is the property of a recurring decimal that is what makes it interesting!
so 0.999999... = 1Exactly!
2006-11-14 19:22:25 · answer #3 · answered by usarora1 3 · 0⤊ 0⤋
actually it cannot be changed into a fraction for eg:
all recurring integers like 0.111111111111... ; 0.2222222222....... etc. are changed into fraction as 1/9 ; 2/9 etc.
so lets take 1/9 = 0.1111111111111111...........
multiply LHS by 9 we get 0.999999999999..........
but on RHS we get 9/9 = 1
so it cannot be converted to fraction
2006-11-14 19:13:25 · answer #4 · answered by yog 2 · 0⤊ 3⤋
It is less than 1 (by some 0.00000...1)
Since it is recurring the fraction will also have recurring digits,
999999999... / 1000000000...
2006-11-15 00:36:14 · answer #5 · answered by Ram 1 · 0⤊ 1⤋
1-0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999..........................................................
=0.00000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...............................................................................1
let x=0.99999999999999999999999999999999999
10x=9.99999999999999999999999999999999999
subtracting
9x=9 and so x=1
1-0.9999999999999999999999999999999999999999999999999
is practically 0
0 is nothing but too insignificant a quantity to be considered
2006-11-14 19:00:35 · answer #6 · answered by raj 7 · 1⤊ 0⤋
it's equal to 1 when you round it off. but if you want to change it to fraction, it's 99/100.
2006-11-14 19:06:04 · answer #7 · answered by athena 2 · 0⤊ 4⤋
no it is not 1
10/11 is the answer;
2006-11-14 19:29:02 · answer #8 · answered by sandywin2006 1 · 0⤊ 4⤋
it is 1 for a proof please refer to
2006-11-14 21:39:35 · answer #9 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
.9999999999999999999............................ multiply by 100000000000000000000000000.................... and divide by the amount of you had multiplied and reduce your answer to lowest term
2006-11-14 19:12:23 · answer #10 · answered by ping2 1 · 0⤊ 2⤋