please explain me how 0.999999999... a nonterminating number as when it is converted into rational number the answer comes out to be 1. Please explain each and every PART of the question
2007-11-30 19:14:13 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
let x = 0.999..
multiply both sides by 10
10x = 9.999...
subtract x = 0.999.
9x = 9
divide by 9
x = 1
Edit: I just thought of another idea
If you accept that 1/3 = 0.333333... repeating.
Multiply both sides by 3
1 = 0.999999.... repeating
2007-11-30 19:20:49 · answer #1 · answered by Demiurge42 7 · 1⤊ 0⤋
what is 1/3 equal to .... 0.333333, right
so what is 3 * 1/3 = 1/3 + 1/3 + 1/3 equal to ..... 3/3 = 1, right
this is classic
use this fraction representation to make your conclusion
2007-12-01 03:22:04 · answer #2 · answered by Jim L 3 · 0⤊ 0⤋
Because for all intensive purposes, 0.999999999999999999999999999999999......(repeating for all infinity) is 1
Because you just have to add....
0.0000000000000000000000000000000000000000000....(repeat for all infinity) 000001
Which is the smallest possible number. It is by all purposes said to be zero
2007-12-01 03:22:18 · answer #3 · answered by Anonymous · 0⤊ 1⤋
there are so many nines the you have to add a very, very, very small number to get 1, therefore it is equal to one.
2007-12-01 03:29:26 · answer #4 · answered by Anonymous · 0⤊ 1⤋