Well remember that above, x was originally set equal to 0.999999 via x=0.999999, and now we have that x is also equal to 9/9, so that means 0.999999=9/9..and there’s 0.999999 written as a fraction! This fraction, can be reduced further to 1, because anything over itself(other than zero) is 1.

## How do you write 0.999 as a fraction?

**999/1000**.

## How do you convert 0.9999 to a fraction?

**1/1**. Alternatively, 1/9=0.1111…, that is, 9/9=0.9999…

## What is 0.99999 repeating as a fraction?

## How is .99999 equal to 1?

## Does 0.999 really equal 1?

= 1 — the sequence of terminating decimals 0.9, 0.99, 0.999, 0.9999, and so on, converges to 1, so **the repeating decimal 0.9999…** **representing the limit of that sequence, is said to be equal to 1**. The same idea works for any rational number with a repeating infinite decimal expansion.

## Is it true that 0.999 1?

In our current system, we haven’t allowed infinitely small numbers. As a result, **0.999…** **= 1 because we don’t allow there to be a gap between them** (so they must be the same). In other number systems (like the hyperreal numbers), 0.999… is less than 1.

## Does 0.99999 equal one?

This number is equal to 1. In other words, “0.999…” is not “almost exactly” or “very, very nearly but not quite” 1 – rather, “0.999…” and “1” represent exactly the same number.

## Is 1 0.9999 repeating?

= 1 — the sequence of terminating decimals 0.9, 0.99, 0.999, 0.9999, and so on, converges to 1, so **the repeating decimal 0.9999…** **representing the limit of that sequence, is said to be equal to 1**. The same idea works for any rational number with a repeating infinite decimal expansion.

## Is 0.999 repeating equal to 1?

In other words, “0.999…” is not “almost exactly” or “very, very nearly but not quite” 1 – rather, **“0.999…” and “1” represent exactly the same number**. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs.

## How do you turn .333333 into a fraction?

Answer: 0.33333 as a fraction is **1/3**.

## Is 0.99999 infinite?

If the digits in each place are multiplied by their corresponding power of 10 and then added together, one obtains the real number that is represented by this decimal expansion. So the decimal expansion 0.9999… actually represents the infinite sum9/10 + 9/100 + 9/1000 + 9/10000 + …

## Does 0.99999 equal 1?

by the definition above, every element of 1 is also an element of 0.999…, and, combined with the proof above that every element of 0.999… is also an element of 1, the sets 0.999… and 1 contain the same rational numbers, and are therefore the same set, that is, **0.999…** **= 1**.

## Is 0.999 1 false?

In our current system, we haven’t allowed infinitely small numbers. As a result, **0.999…** **= 1 because we don’t allow there to be a gap between them** (so they must be the same). In other number systems (like the hyperreal numbers), 0.999… is less than 1.

## Is 0.9999999999 equal to 1?

= 1 — the sequence of terminating decimals 0.9, 0.99, 0.999, 0.9999, and so on, converges to 1, so the repeating decimal 0.9999… representing the limit of that sequence, is said to be equal to 1. The same idea works for any rational number with a repeating infinite decimal expansion.

## How can you prove 0.999999 is 1?

It’s a proof by contradiction. **There is no E that is greater than zero such that E = (1 — 0.9999…)**. Therefore 0.999… = 1.

## Does 99999 repeating equal 1?

99999… was **never exactly equal to 1**. Instead, a limitation in notation of decimal numbers created the illusion that the two numbers are equal and an academic desire to keep everything neat and tidy lead to confirmation bias and the statement that, at some limit, the actual difference was essentially akin to 0.

## What’s the largest number in the world?

The thing is, infinity is not a number, but a concept or idea. **A “googol” is the number 1 followed by 100 zeroes**. The biggest number with a name is a “googolplex,” which is the number 1 followed by a googol zeroes.

## What is the proof that 0.99999999 is 1?

It’s a proof by contradiction. **There is no E that is greater than zero such that E = (1 — 0.9999…)**. Therefore 0.999… = 1.

## Does infinity have a number?

**Infinity is not a number**, but a concept. We can define infinity as the object that is larger than any other number, but infinity is not a real number itself, since it doesn’t fulfill the same axioms that the real numbers do.

## Is 0.999 infinite?

“But,” you ask, “what about that ‘1’ at the end?” Ah, but **0.999… is an infinite decimal**; there is no “end”, and thus there is no “1 at the end”. The zeroes go on forever. And 0.000… = 0.

## Does 0.999 exist?

Infinity does weird things, and one thing it does is that **the infinitely long decimal expression 0.999…** **turns out to be equal to 1**. The implication is that there are actually many real numbers with two equivalent decimal expressions for them (so 0.5829999… =0.583, for example).

## What proves 0.99999 1?

It’s a proof by contradiction. **There is no E that is greater than zero such that E = (1 — 0.9999…)**. Therefore 0.999… = 1.