I teach 6th grade, but I would consider my class advanced prealgebra. It is included in lessons on rational vs. irrational numbers. My students estimate square roots as well.

This is voodoo witchcraft. Should be on religion/theology board.

That's good stuff. I had a math teacher in high school who used to be a calculator at General Dynamics. She taught us all sorts of shortcuts but not that one. Thanks.

Mathguy64 said:

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X=.823232323. . .
10x=8.232323
1000x=823.232323
1000x-10x=815
990x=815
X=815/990=163/198

Sum of digits = 361

What do I win?

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I'm going to show this to my kid. I gave you a blue star, that is all I can afford.

Take your 98 and skip it!!!

Let x = 0.82323232 ...

Then 100x = 82.323232...

100x-x = 82.323232...-0.82323232...

99x = 81.5

Thus, x = 81.5/99 or 163/198

Mathguy64 said:

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X=.823232323. . .
10x=8.232323
1000x=823.232323
1000x-10x=815
990x=815
X=815/990=163/198

Sum of digits = 361

What do I win?

---

Ahhh. You beat me to it.

I learned this approach in high school.

I just multiply by 10^n where n is the number of repeating digits. Then subtract and simply into integers from there.

redline248 said:

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Wow, I have never seen that repeating decimal to fraction before (either way). In what grade level would that have been taught so I can properly direct my anger at the responsible teacher.

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Freshman algebra -- in high school.

I don't remember if we had one year or two years of high school algebra. If we had two years, it might have been the sophomore year. I think that was the geometry year, though.

I don't understand the notion of adding the numerator to the denominator. That sounds rather meaningless to me. Off of the top of my head, I can't imagine any reason that anyone would ever find a reason to add a numerator and a denominator together.

Not that there is anything wrong with pointless exercises in math. For example, in church, one the first things I do when the service starts is to calculate (in my head) the average of the hymn numbers for the service.

eric76 said:

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I don't understand the notion of adding the numerator to the denominator. That sounds rather meaningless to me. Off of the top of my head, I can't imagine any reason that anyone would ever find a reason to add a numerator and a denominator together.

Not that there is anything wrong with pointless exercises in math. For example, in church, one the first things I do when the service starts is to calculate (in my head) the average of the hymn numbers for the service.

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It's a way to turn the problem into a multiple choice answer set and to eliminate working it backwards.

eric76 said:

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redline248 said:

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Wow, I have never seen that repeating decimal to fraction before (either way). In what grade level would that have been taught so I can properly direct my anger at the responsible teacher.

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Freshman algebra -- in high school.

I don't remember if we had one year or two years of high school algebra. If we had two years, it might have been the sophomore year. I think that was the geometry year, though.

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Ok, so I took algebra 1 in 8th grade and it's possible this was covered, but given it was in podunk 3A school district, I can't say for sure. I also barely remember anything from 8th grade.

Encryption techniques.

redline248 said:

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eric76 said:

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redline248 said:

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Wow, I have never seen that repeating decimal to fraction before (either way). In what grade level would that have been taught so I can properly direct my anger at the responsible teacher.

---

Freshman algebra -- in high school.

I don't remember if we had one year or two years of high school algebra. If we had two years, it might have been the sophomore year. I think that was the geometry year, though.

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Ok, so I took algebra 1 in 8th grade and it's possible this was covered, but given it was in podunk 3A school district, I can't say for sure. I also barely remember anything from 8th grade.

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We were 1A.

TexasRebel said:

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Encryption techniques.

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Maybe for some kind of hashing scheme, but not real likely.

For encrypting message, remember that you would need to decrypt the message as well. Given the sum of a numerator and denominator, you would presumably need to be able to back out of it provided you knew the key. In encryption, you are generally doing so with large numbers of digits. Would you really want to have to try every possible combination of numerators and denominators to figure out which specific numerator and denominator it was for that sum? Admittedly, that operation would be O(x), but still that would slow down decryption.

Anything that'll slow down decryption by an unknown party is good.

If the intended decryptor has one side, there is no searching.

TexasRebel said:

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Anything that'll slow down decryption by an unknown party is good.

If the intended decryptor has one side, there is no searching.

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Like a one time pad? Does anyone still use those?

Cool beans