Is 495.5 Equal to 495? A Mathematical Proof

  • Thread starter zeromodz
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In summary: Sorry for doubting your originality, Werg!In summary, the conversation discussed the operations on infinite decimal representations and the incorrectness of certain equations involving them. The correct equation for 99.9999... - 0.9 is 99.1. However, this may lead to a debate on the equality of 0.9999... and 1.
  • #1
zeromodz
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Sorry, I typed the wrong thing in the title, I meant 495.5 = 495

(1/3) + (1/3) + (1/3) = 1
(0.333333333333) + (0.33333333333) + (0.33333333333) = 1
0.999999999999999 = 1
99.9999999 = 100 (Multiplied by 10)
99.1 = 99 (Subtracted 0.9)
495.5= 495 (Multiplied by 5) <---------------PROOF
 
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  • #2
Operations on infinite decimal representations need to be considered more carefully.
 
  • #3
99.9999999 = 100 (Multiplied by 10)
99.1 = 99 (Subtracted 0.9)

This is not how subtraction is done

100-.9=99?

99.9999999... -.9=99.1?

Both wrong. Even if we assume that you flipped the equation so 100-.9=99.1, 99.99999-.9 is not 99
 
  • #4
Office_Shredder said:
This is not how subtraction is done

100-.9=99?

99.9999999... -.9=99.1?

Both wrong. Even if we assume that you flipped the equation so 100-.9=99.1, 99.99999-.9 is not 99

The second one is right.
 
  • #5
Werg22 said:
Office_Shredder said:
This is not how subtraction is done

100-.9=99?

99.9999999... -.9=99.1?

Both wrong. Even if we assume that you flipped the equation so 100-.9=99.1, 99.99999-.9 is not 99
The second one is right.

Umm... both 100-.9=99 and 99.999...-.9=99.1 are wrong. So I don't know what you're on about, plus it would've been a lot easier for the reader to determine which "second one" you're talking about by quoting just the relevant equality, not the entire post.
 
  • #6
Mentallic said:
Umm... both 100-.9=99 and 99.999...-.9=99.1 are wrong. So I don't know what you're on about, plus it would've been a lot easier for the reader to determine which "second one" you're talking about by quoting just the relevant equality, not the entire post.

No, 99.9999...-0.9 = 99.0999... = 99.1 is correct.
 
  • #7
Mentallic said:
Umm... both 100-.9=99 and 99.999...-.9=99.1 are wrong. So I don't know what you're on about, plus it would've been a lot easier for the reader to determine which "second one" you're talking about by quoting just the relevant equality, not the entire post.

There was nothing wrong with what Werg said. Yes [itex](99.9999... - 0.9)[/itex] really is equal to 99.1.

I can't believe this senseless OP is going to come back to yet another [itex]0.9999... \neq 1[/itex] debate. :confused:
 
  • #8
Oh yes of course, I didn't even stop to think about it once I saw all the recurring decimal places were cut off.
 

FAQ: Is 495.5 Equal to 495? A Mathematical Proof

How can you prove that 495 is equal to 499.5?

To prove that 495 is equal to 499.5, we can use the basic algebraic equation x + y = z, where x is 495, y is 4.5, and z is 499.5. This equation demonstrates that 495 and 499.5 are equivalent values.

What mathematical concepts can be used to prove this equation?

The concept of equality, addition, and basic algebra can be used to prove that 495 is equal to 499.5. We can also use the commutative and associative properties of addition to rearrange the numbers in the equation.

Can you provide a visual representation of this equation?

Yes, we can represent the equation visually using a number line or a bar model. On a number line, we can show that 495 and 499.5 are both located at the same point on the line, indicating that they are equal. In a bar model, we can represent 495 and 499.5 as equal lengths, again demonstrating their equivalence.

How does this proof apply to real-world situations?

In real-world situations, this proof can be used to show that two different values or quantities are equivalent. For example, if a recipe calls for 495 grams of flour and you only have 499.5 grams, you can use this proof to show that they are essentially the same amount and will not significantly impact the outcome of the recipe.

What other examples can be used to demonstrate this equation?

Other examples that can demonstrate this equation include converting measurements, such as 495 milliliters to 499.5 milliliters, or converting currencies, such as 495 US dollars to 499.5 Canadian dollars. In each case, the values may be different, but they are equal in terms of their numerical value.

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