Is 0.9999999 1 Can you prove it?
Yes, at any given stop, at any given stage of the expansion, for any given finite number of 9s, there will be a difference between 0.999… 9 and 1. That is, if you do the subtraction, 1 – 0.999… 9 will not equal zero.
Which of the following is true for the value of 0.999 A It is equal to 1 B it is less than 1 C it is equal to 0.9 d None of the above?
Step by step explanation : The number 0.999 is more than 0.9 and its nearly to 1. So, we can’t say that the 0.999 is equal to 0.9 or 1.
Is 0.9999999 an irrational number?
One of them says that a rational number is that which is non-terminating (a number which cannot be terminated) and repeating . So 0.99999…. aquires both repeating and non-terminating property . Hence it is a rational number .
What does 0.99999 mean?
INFINITE LIMIT
0.99999… is SHORTHAND FOR AN INFINITE LIMIT! So I the infinite definition of a limit is the appropriate way to understand it. When we learn decimal notation, we haven’t learned the limit yet.
Is 0.99 a rational number?
9*1/9=0.999… This proves both that 1=0.999… and therefore 0.999… is rational!
Is 0.222222 a rational number?
The very nicest rational numbers are those with a finite number of digits in their decimal form. Any rational number with a divisor that is not a multiple of 2s and 5s will repeat forever. The simplest ones are the ninths. 1/9=0.111111 …, 2/9=0.222222 …, and so on.
What is 99999 repeating as a fraction?
=> X =99 /99 =1 (as a fraction 1 can be written as 1/1). More correctly, . 99999 repeating is equivalent to 1.
What is the difference between 1 and 99999?
The Actual Answer: Hyperreal Numbers. We all know that .99999… is not actually equal to 1, but that the difference between the two numbers is so infinitesimally small that it “doesn’t really matter”. Well, the true notation of equality between 1 and .99999… is 1 -h = .99999… and that is not an actual equality between the two numbers.
How do you write the number 999999 as a sequence?
Strictly speaking, 0.99999 written exactly as such (assuming decimal notation) is defined as the finite sequence 9 × ∑ k = 1 5 10 − k = 9 × ( 1 10 + 1 100 + 1 1 000 + 1 10 000 + 1 100 000) ≠ 1. That said, if you put three dots after the last 9, and write it as 0.99999 …, or similar, you then imply that the 9 s go on forever.
What is 3/3 equal to 99999?
One of the most simplistic arguments that .99999… = 1 is that 1/3 = .33333… and if you multiply both by 3, you get the answer that 3/3 = .99999… Since 3/3 is obviously 1, .99999… must therefore also = 1.
Is a zero equivalent to an integer?
Consider the real number that is represented by a zero and a decimal point, followed by a never-ending string of nines: 0.99999… It may come as a surprise when you first learn the fact that this real number is actually EQUAL to the integer 1. A common argument that is often given to show this is as follows.