Are these equal?
These two numbers are very close together:
3 5 3 1 2 2 ≈ 0 . 3 4 5 6 , 2 1 7 7 5 ≈ 0 . 3 4 5 6
Which of these numbers is larger?
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5 solutions
Moderator note:
Yes. Bonus question: Since you already know the answer, can you prove that 2 1 7 7 5 > 3 5 3 1 2 2 by contradiction?
This solution is not mine , it is found here . ( i am the thread starter)
Suppose that 3 5 3 1 2 2 ≥ 2 1 7 7 5 Then 3 5 3 1 2 2 − 2 1 7 7 5 3 5 3 × 2 1 7 2 1 7 × 1 2 2 − 3 5 3 × 7 5 2 6 4 7 4 − 2 6 4 7 5 − 1 ≥ 0 ≥ 0 ≥ 0 ≥ 0
does this count as contradiction? it looks just like saying show 2>1 then assume 2<1 --> 1<0 (impossible) , therefore it is 2>1
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Yes you are correct indeed Ne-ko.Well done!
Haha, they saw it here and copied it there.
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yeap , i saw it here , and i don't know how to solve using contradiction.
so i post it there , after all this page here is meant for solution isnt it? i cant just simply ask at here.....
That doesn't actually added much. It's glib!
suppose, 122/353 ? 75/217 or ,122×217 ? 75×353 or, 26474 ? 26475 so, 26474 < 26475 so, 75/217 is larger one .
122/353 is 0.345609 but 75/217 is 0.345622 ..... hence second one is greater ...!!
Moderator note:
It's more difficult to perform long division compared to cross multiplication right?
The accuracy is 1/10000. So. 122 x 217 has result with last number is 4 (xxxx4) and 75 x 353 has the last number is 5 (xxxx5). So. 122 x 217 < 75 x 353 because of 4 < 5
Let A = 3 5 3 1 2 2 and B = 2 1 7 7 5 then A - B < 0 this imply B > A
3 5 3 × 7 5 = 2 6 4 7 5 ≥ 1 2 2 × 2 1 7 = 2 6 4 7 4
The rest is obvious I believe .Nice question by the way!