Is 495.5 Equal to 495? A Mathematical Proof

  • Context: High School 
  • Thread starter Thread starter zeromodz
  • Start date Start date
  • Tags Tags
    Proof
Click For Summary
SUMMARY

The discussion centers on the mathematical assertion that 495.5 equals 495, which is proven incorrect through various examples involving infinite decimal representations. Participants clarify that operations involving numbers like 0.9999... and 99.9999999 must be handled with precision, emphasizing that 99.9999... - 0.9 equals 99.1, not 99. The conversation highlights common misconceptions in subtraction and decimal representation, ultimately reinforcing the importance of understanding limits and infinite series in mathematics.

PREREQUISITES
  • Understanding of infinite decimal representations
  • Basic knowledge of arithmetic operations, particularly subtraction
  • Familiarity with limits in calculus
  • Concept of recurring decimals and their equivalence
NEXT STEPS
  • Study the properties of infinite series in calculus
  • Learn about the concept of limits and their applications
  • Explore the mathematical proof of 0.9999... = 1
  • Investigate common misconceptions in arithmetic operations involving decimals
USEFUL FOR

Mathematicians, educators, students, and anyone interested in understanding the nuances of decimal representation and arithmetic operations.

zeromodz
Messages
244
Reaction score
0
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
 
Mathematics news on Phys.org
Operations on infinite decimal representations need to be considered more carefully.
 
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
 
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.
 
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.
 
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.
 
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 (99.9999... - 0.9) really is equal to 99.1.

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

Similar threads

High School Weird stuff on infinite numerical sequences in a Soviet book
  • · Replies 5 ·
Replies
5
Views
1K
High School Creating Log Tables: Briggs' 400-Year-Old Accomplishment
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Can the Infinite Sum of Natural Numbers Really Equal -1/12?
  • · Replies 6 ·
Replies
6
Views
4K
High School Are Inverse Problems More Complex Than Direct Problems in Mathematics?
  • · Replies 13 ·
Replies
13
Views
3K
High School Index numbers vs. Quantity in a group
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Proving an Identity: Is my High School Explanation Correct?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate RIP Yvonne Choquet-Bruhat (1923-2025)
  • · Replies 4 ·
Replies
4
Views
918
High School How does this derivative work? And why the speed of light remains?
  • · Replies 7 ·
Replies
7
Views
407
High School How to Add Metres & Seconds for Equal ds2: Einstein's Theory
  • · Replies 22 ·
Replies
22
Views
2K
Undergrad Playing with math keeps me sharp
  • · Replies 6 ·
Replies
6
Views
3K