Does 0.999... Eqaul 1??
2008-05-05 10:06 am
I would like peoples idea and thoughts on the statement that 0.9 recurring is eqaul to 1.
回答 (10)
2008-05-05 10:09 am
✔ 最佳答案
Yes.If you think it does not, can you name a number between 0.9999..... and 1?
x = 0.9999.....
10x = 9.9999.....
10x = 9 + 0.9999.....
10x = 9 + x
9x = 9
x = 1
0.99999......
= 9/10 + 9/100 + 9/1000 + .....
This is an infinite geometric series
a = 9/10
r = 1/10
Sum = a/(1-r)
= (9/10) / (1 - 1/10)
= (9/10) / (9/10)
= 1
0.9999...... recurring is EXACTLY equal to 1.
2008-05-05 10:13 am
0.999... = 1 ?
x = 0.999......
10x = 9.999......
10x - x = 9.999...... - 0.999......
9x = 9
x = 9/9
x = 1
∴ 0.999...... = 1
x = 0.999......
10x = 9.999......
10x - x = 9.999...... - 0.999......
9x = 9
x = 9/9
x = 1
∴ 0.999...... = 1
2008-05-05 10:14 am
No, 0.9999999999999999... is not equal to 1.
It might be, to a acceptable margin of error, be "the same as", or "near enough to", or "about" 1, but it can never be "equal" to 1.
An engineer you say "Yes", but a mathematician would not.
Thats why they had to rebuild the Millennium Bridge. (No, this is not the reason, but you get the point.)
It might be, to a acceptable margin of error, be "the same as", or "near enough to", or "about" 1, but it can never be "equal" to 1.
An engineer you say "Yes", but a mathematician would not.
Thats why they had to rebuild the Millennium Bridge. (No, this is not the reason, but you get the point.)
2008-05-05 10:10 am
no, numbers r simple and factual. unless the number looks exactly the same then it is not equal. .9999 is roughly close but not equal.
2008-05-05 10:29 am
see http://en.wikipedia.org/wiki/0.999... for more details
-edit-
also search for the internet about 0.999... because you will find that 0.999 = 1.
for those who tell you that they are not equal, don't believe them because maybe they didn't know the fact why 0.999... = 1
-edit-
also search for the internet about 0.999... because you will find that 0.999 = 1.
for those who tell you that they are not equal, don't believe them because maybe they didn't know the fact why 0.999... = 1
2008-05-05 10:35 am
Yes, the two are exactly equal.
Quick proof:
1/3 = 0.333333.....
so 3*1/3 = 1 = 0.99999....
.
Quick proof:
1/3 = 0.333333.....
so 3*1/3 = 1 = 0.99999....
.
2008-05-05 10:29 am
1/9 = .111...
so:
if x = 1/9
x = .111...
9x = .999...
9*1/9 = .999...
1 = .999...
so:
if x = 1/9
x = .111...
9x = .999...
9*1/9 = .999...
1 = .999...
2008-05-05 12:46 pm
0.99999.... is a recurring number, but will never EXACTLY be equal to 1. IIf asked to round off to nearest whole number, yes it would equal to one, but factually, it never equals exactly to 1!
2008-05-05 10:19 am
No. It's not equal to 1. Only for approximation purpose, many round off to 1.
2008-05-05 10:09 am
For all intents and purposes concerning real-life problems, yes it is.
For exact measurement's sake, no. 1 = 1, no other number does.
But a toddler could have known that.
For exact measurement's sake, no. 1 = 1, no other number does.
But a toddler could have known that.
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