Why 0.99999 is 1?

The meaning of the notation 0.999... is the least point on the number line lying to the right of all of the numbers 0.9, 0.99, 0.999, etc. Because there is ultimately no room between 1 and these numbers, the point 1 must be this least point, and so 0.999... = 1.

Why is 0.999999 equal to 1?

Consider the real number that is represented by a zero and a decimal point, followed by a never-ending string of nines: 0.99999… and therefore S=1.

How do you prove 0.9999 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.

Is .9 repeating the same as 1?

It's the same thing with . 9 repeating, which equals 1. Those are two ways of writing the same number. If you do .

Is 0.999 1 false?

Why some people say it's false: It's less than one, since it starts with 0.99 instead of 1.00. So it cannot be equal to 1. The statement 0.999 … = 1 0.999 \ldots = 1 0.

Does 0.999... = 1?

Is 0.99999 1 True or false?

Yes,it is one. The prof is very simple: 1/3 = 0.3333333… But if you mean just 0.99999, then it is not one.

Is .999 less than 1?

In particular, a terminating infinite decimal . 999 ...; ... 999 is less than 1.

How is .99999 equal to 1 Reddit?

0.9, 0.99, 0.999, 0.9999, ... limits to 1, because the difference between the two tends to 0. so 0.9999... = 1.

Can you represent 0.9999999 as a fraction?

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.

Can you add 1 to infinity?

If you add one to infinity, you still have infinity; you don't have a bigger number. If you believe that, then infinity is not a number.

Is 1 0.9 True or false?

No. If these two quantities were equal the difference between them would be zero, but 1 - 0.90 = 0.10 and so 1 does not equal 0.90.

Why is infinity not a number?

Infinity is not a real number, it is an idea. An idea of something without an end. Infinity cannot be measured. Even these faraway galaxies can't compete with infinity.

What is 1 infinity equal to?

Infinity is a concept, not a number; therefore, the expression 1/infinity is actually undefined.

Why is 0.99 repeating equal to 1?

The meaning of the notation 0.999... is the least point on the number line lying to the right of all of the numbers 0.9, 0.99, 0.999, etc. Because there is ultimately no room between 1 and these numbers, the point 1 must be this least point, and so 0.999... = 1.

Why is a number times 1 always equal to itself?

The identity property of 1 says that any number multiplied by 1 keeps its identity. In other words, any number multiplied by 1 stays the same. The reason the number stays the same is because multiplying by 1 means we have 1 copy of the number.

Is .999 the smallest value?

0. 9 is the smallest number .

What is .99999 repeating as a fraction?

And 9x = 9, you can now write x as a fraction equal to 9/9 or basically 1. Hence . 99999 repeating is equal to 1.

How do you turn 0.9999 into a fraction?

Since 0.9999… =1, it can be expressed in fraction form as 1/1. Alternatively, 1/9=0.1111…, that is, 9/9=0.9999…

How does 0.9 as a fraction work?

Answer: 0.9 as a fraction is written as 9/10

0.9 is a decimal number. Explanation: To convert a decimal number into a fraction, we write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the number of zeros required accordingly.

Why is 9999 1?

9999 denotes 9,999/10,000, i.e., 1 minus 1/10,000. The more 9's one adds, the closer one is to 1; each additional 9 cuts the difference from 1 by a factor of 10, but no finite number of 9's brings one exactly to 1. People hear such expressions frequently, and may not realize the subtle distinction between .

Is 9.9 repeating equal to 10?

9.999… and 10 aren't different numbers, they're the same number written different ways.

What does 1 0 actually equal?

Now this statement is most commonly (though not correctly) referred to as 1/0 = infinity and is so common in mathematics and physics that people working/studying in this field take limits to be obvious.

What is 0.999 as a fraction?

Solution: 0.999 as a fraction is 999/1000.

Is 0.999 a rational number?

Second, any number whose decimal expansion repeats itself is rational, in our case, 0.999… is an infinite repetition of 9, so 0.999… is rational.

What number is between 0.999 and 1?

There are no numbers between 1 and 0.999… (if the nine's are repeating to infinity), because 1 is exactly equal to 0.999… (with infinitely repeating 9's ). In other words, just like “,” “,” “,” or “,” these are simply two other different ways to write down the exact same thing… 1.