As the photo above shows, the following equation:
1 2 8 e 9 8 0
gives the message "I Love You" when half of it is erased. However, what is the value of 1 2 8 e 9 8 0 when rounded down to one decimal place?
Photo credits: iblogangela
Details and assumptions: e 9 8 0 is defined as e × 9 8 0 .
Please try not to use a calculator for this.
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The solution to this problem is trivial and is left as an exercise to the reader.
whats the solution??
Seriously... No solutions??
Same what I did
When did nobita get this smart.? He used to fail in all subjects .
t h e v a l u e o f e i s 2 . 7 1 8 s o , 2 . 7 1 8 × 9 8 0 = 2 6 6 3 . 9 1 6 n o w , 2 6 6 3 . 9 1 6 = 5 1 . 6 1 3 h e n c e , a n s w e r i s 1 2 8 × 5 1 . 6 1 3 = 6 6 0 6 . 4 6
what is actually e?
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Eulers number is a value that represents a number summing itself infinitely small so 1+.5+.25 etc. eventually you get 2.718 blah blah blah.
You can treat it as a constant because it is used as a multiplier to find what the value of a specific number would be in that scenario or that particular type of compounding which is common in nature I suppose.
Anyways, this answer isn't completely accurate so if someone is willing to give a detailed explanation while correcting mine, that'd be great ; )
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Euler's number is the limit as n approaches infinity of (1+1/n)^n or the infinite series of 1/n!. It is the number that is the base for continuous interest and it shows up in a lot of other cool places like e^(i*pi)+1=0.
Euler's number, a mathematical constant.
Then I used a calculator to check and get 6606.13
this person don't want us to use a calculator, but it does not stop us from using pen and paper...it however took three turns to get to correct answer
1 2 8 e ∗ 9 8 0 = 1 2 8 e ∗ 2 2 ∗ 5 ∗ 7 2 = 1 2 8 ∗ 1 4 e ∗ 5 = 1 7 9 2 e ∗ 5
at which point we can approximate e =2.718 then use guess &check method to approximate square root
≈ 1 7 9 2 2 . 7 1 8 ∗ 5 = 1 7 9 2 ∗ s q r t ( 1 3 . 5 9 ) ≈ 1 7 9 2 ∗ 3 . 6 8 5 = 6 6 0 3 . 5 and checking with calculator 1 7 9 2 e ∗ 5 = 6 6 0 6 . 4 8
I really don't know is there any solution for this without using a calculator?
Yes, one that'd involve tedious calculations.
Plugging this equation into a calculator gives the value 6606.48188... which should round up to 6606.5, no?
I said rounded down...
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@Charlton Teo how you did it without using calculator?
its 6606.1393
For anyone still doing those here is the solution I entered : 6528 (and got correct, I know it's not the right value but it's an honest approximation to me). How I got to that number : e ≈ 2 . 7 = 2 7 / 1 0 9 8 0 × e ≈ 2 7 × 9 8 = 2 7 × 1 0 0 = 3 × 9 × 1 0 0 s q r t ( e 9 8 0 ) ≈ 3 × 1 0 × s q r t ( 3 ) = 3 0 × s q r t ( 3 ) s q r t ( 3 ) ≈ 1 . 7 3 0 ∗ 1 2 8 = 3 8 4 0 1 2 8 s q r t ( e 9 8 0 ) ≈ 1 2 8 ∗ 3 0 ∗ 1 . 7 = 6 5 2 8 Sorry about any bad presentation, I'm not used to do this.
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Use a calculator. I obviously do not understand English.