Accuracy up to how many decimals...........?

[mathspassion]

Accuracy up to how many decimals...........?

 

3² + 4² = 5²

9 + 16 = 25

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1.(3/4)² + (4/4)² = (5/4)²

0.75² + 1² = 1.25²

0.5625 + 1 = 1.5625

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2.(3/5)² + (4/5)² = (5/5)²

0.6² + 0.8² = 1²

0.36 + 0.64 = 1

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O.K. Fellas, let’s notice a difference here.

3.(3/3)^2 +(4/3)^2  = (5/3)^2

1^2 + 1.3^2 = 1.6^2

1 + 1.69 = 2.56

Difference => 2.69 – 2.56 = 0.13

Accuracy =>0.13/2.69=.048

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4.(3/3)^2 +(4/3)^2  = (5/3)^2

1^2 + 1.33^2 = 1.66^2

1 + 1.7689 = 2.7556

Difference => 2.7689 – 2.7556 = 0.133

Accuracy => 0.133/2.7689 = 0.0048

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5.(3/3)^2 +(4/3)^2  = (5/3)^2

1^2 + 1.333^2 = 1.666^2

1 + 1.776889 = 2.775556

Difference => 2.776889 – 2.775556 = 0.001333

Accuracy => 0.001333/2.776889 = 0.00048

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6.(3/3)^2 +(4/3)^2  = (5/3)^2

1^2 + 1.3333^2 = 1.6666^2

1 + 1.77768889 = 2.77755556

Difference => 2.77768889 – 2.77755556 = 0.00013333

Accuracy => 0.0001333/2.77768889 = 0.000048

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7.(3/3)^2 +(4/3)^2  = (5/3)^2

1^2 + 1.33333^2 = 1.66666^2

1 + 1.7777688889 = 2.7777555556

Difference => 2.7777688889 – 2.7777555556 = 0.000013333

Accuracy => 0.000013333/2.7777688889 = 0.0000048

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8.(3/3)^2 +(4/3)^2  = (5/3)^2

1^2 + 1.333333^2 = 1.666666^2

1 + 1.777776888889 = 2.777775555556

Difference => 2.77777688889 – 2.777775555556 = 0.0000013333

Accuracy => 0.0000013333/2.777776888889 = 0.00000048

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So, as you can see its pretty much visible here that irrespective of the precision there is in division, the presence of digits 4 and 8 in the Accuracy Factor is mesmeric to look. This may come under Number Pattern Theory where the operation eventually leads to same numerical digits though quantitatively they are different.

 Author: Piyush Goel

[Sensei]

18 minutes ago, mathspassion said:

1^2 + 1.3^2 = 1.6^2

4/3 = 1.33333333(3)

5/3 = 1.66666666(6)

1 + 1.33333333(3)^2 = 1.66666666(6) ^2

1 + 1.777777777777777777777777777777(7) = 2.777777777777777777777777777777(7)

 

also:

(4/3)^2 = 16/9

(5/3)^2 = 25/9

9/9 + 16/9 = 25/9

(lowest common denominator)

 

[mathspassion]

On 5/22/2018 at 3:41 PM, Sensei said:

4/3 = 1.33333333(3)

5/3 = 1.66666666(6)

1 + 1.33333333(3)^2 = 1.66666666(6) ^2

1 + 1.777777777777777777777777777777(7) = 2.777777777777777777777777777777(7)

 

also:

(4/3)^2 = 16/9

(5/3)^2 = 25/9

9/9 + 16/9 = 25/9

(lowest common denominator)

 

what u write we all know my question is up to how many decimals.......o.k.        why not trying to understand.