Verify if 0.9999 is Equal to 1

  • Thread starter LastTimelord
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In summary, comparing 0.9999 and 1 is important because they are two numbers that are extremely close in value and can often be confused as equal. However, they are actually two ways of representing the same number in decimal form. There are multiple ways to prove their equality, and there are real-life examples that demonstrate this as well. It is not possible for 0.9999 to be slightly different from 1 due to the limitations of decimal notation.
  • #1
LastTimelord
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Is 0.9999... equal to 1?

I think it is, but there are several sources arguing that statement.

Could you verify this?
 
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https://www.physicsforums.com/showthread.php?t=507002 [Broken]andhttps://www.physicsforums.com/showthread.php?t=507001 [Broken]
 
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  • #3


Oh thank you, I hadn't realized that other people had posted this.
 

1. What is the significance of comparing 0.9999 and 1?

Comparing 0.9999 and 1 is important because they are two numbers that are extremely close in value and can often be confused as equal. It is necessary to verify their equality in order to avoid any misunderstandings or errors in calculations.

2. How can 0.9999 and 1 be equal if they are different numbers?

Although they may appear different, 0.9999 and 1 are actually two ways of representing the same number in decimal form. This is due to the nature of decimal notation, where numbers can have infinite repeating digits. In this case, the number 0.9999 is equal to 1.

3. Can you prove that 0.9999 is equal to 1?

Yes, there are multiple ways to prove that 0.9999 is equal to 1. One way is to use algebra and show that 0.9999 is equivalent to 1 by subtracting 1 from both sides of the equation. Another way is to use the concept of limits in calculus, where the limit of 0.9999 as it approaches infinity is equal to 1.

4. Are there any real-life examples that demonstrate the equality of 0.9999 and 1?

Yes, there are many real-life examples that illustrate the equality of 0.9999 and 1. One example is the concept of repeating decimals in the measurement of time. For instance, 1 hour is equal to 60 minutes, which is represented as 0.9999 hours in decimal form. Another example is the use of repeating decimals in monetary values, such as $0.9999 being equal to $1.

5. Is it possible for 0.9999 to be slightly different from 1?

No, it is not possible for 0.9999 to be slightly different from 1. As mentioned earlier, 0.9999 and 1 are two ways of representing the same number and are therefore exactly equal. Any perceived difference between the two numbers is due to the limitations of decimal notation, which can only show a finite number of digits.

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