... A good day to you Newton, The question is to convert 10.135353... to a fraction (mixed number or improper fraction), so to 10 .../... I fully understood your strategy with a geometric series, but isn't there a shorter way? The way I would solve this conversion is as follows: STEP 1) Put the 10 aside and just work on 0.135353... STEP 2) let X = 0 .135353... so, 10X = 1.35353... and 1000X = 135.35353... STEP 3) Subtract 10X from 1000X to get rid of 0.35353... so, 1000X - 10X = 135.35353... - 1.35353... = 135 - 1 = 134, we obtain the equation 990X = 134 ... X = 134/990 = 67/ 495 STEP 4) NOT FORGETTING to add the 10 we put aside to X = 67/495: 10 + 67/495 = 10 67/495 (mixed number form) = 5017/495 (improper fraction form) ... Of course you already know all this, but I just wanted the exercise to be less abstract looking too (lol) ... I'm glad to see you're still doing well my friend Newton, and from now on I shall never forget that 2 and 2 equals 4 (lol) ... Take very good care, Jan-W p.s. I'm going to a street party today, we are celebrating Freedom Day today in Holland, meaning the end of WW II 78 years ago ...
Happy Celebrations, my friend. I agree 100% with you on that method. That is how I did the previous video. It is less abstract too. Just algebra and I love it. I am glad you are well and safe. Good to hear from you.
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0.03535 recurring the 35 is repeating as a fraction It’s 35/990 which can be reduced to 7/198.
Input interpretation
35/10^3 + 35/10^5 + 35/10^7 + ... = 7/198
Results
True
True
Logarithmic form
log(198, 35/10^3 + 35/10^5 + 35/10^7 + ...) = log(198, 7) - log(198, 198)
... A good day to you Newton, The question is to convert 10.135353... to a fraction (mixed number or improper fraction), so to 10 .../... I fully understood your strategy with a geometric series, but isn't there a shorter way? The way I would solve this conversion is as follows: STEP 1) Put the 10 aside and just work on 0.135353... STEP 2) let X = 0 .135353... so, 10X = 1.35353... and 1000X = 135.35353... STEP 3) Subtract 10X from 1000X to get rid of 0.35353... so, 1000X - 10X = 135.35353... - 1.35353... = 135 - 1 = 134, we obtain the equation 990X = 134 ... X = 134/990 = 67/ 495 STEP 4) NOT FORGETTING to add the 10 we put aside to X = 67/495: 10 + 67/495 = 10 67/495 (mixed number form) = 5017/495 (improper fraction form) ... Of course you already know all this, but I just wanted the exercise to be less abstract looking too (lol) ... I'm glad to see you're still doing well my friend Newton, and from now on I shall never forget that 2 and 2 equals 4 (lol) ... Take very good care, Jan-W p.s. I'm going to a street party today, we are celebrating Freedom Day today in Holland, meaning the end of WW II 78 years ago ...
Happy Celebrations, my friend. I agree 100% with you on that method. That is how I did the previous video. It is less abstract too. Just algebra and I love it. I am glad you are well and safe. Good to hear from you.
10.1353535 recurring=10 67/495=5017/495 It’s in my head.
101/10+35/990=5017/495=10 67/495