Universal, all around way to get decimals to fractions?

[HazeTheBeater]

Hey everyone! Thanks a lot for the past help in my other post.

Right now I am studying arithmetics with a McGrawHill book, and they seem to have a lot of get-arounds for all the types of decimals that exist.
They have 3 different ways to convert decimals and for different exceptions. I believe this is inefficient and most likely troublesome to remember because
you gotta go like : If this is this, then that, or if it is that, then this and that.
Thats a lot of trouble for me, does anyone know of a way to do this without too much hassle that includes a way for bar notation decimals, normal decimals and 0.00 decimals?

 

[Dr.Peterson]

Can you show us the three methods (and the "get-arounds", if they are different)? I'm not sure what you mean by "normal" and "0.00", and even if I did, I might assume a different method than the ones you are objecting to.

I think you have to use a different method for repeating decimals (bar notation), because they can't be written in a terminating form as the others presumably are.

 

[HazeTheBeater]

T

Can you show us the three methods (and the "get-arounds", if they are different)? I'm not sure what you mean by "normal" and "0.00", and even if I did, I might assume a different method than the ones you are objecting to.

I think you have to use a different method for repeating decimals (bar notation), because they can't be written in a terminating form as the others presumably are.

This is what my book says

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[HazeTheBeater]

Can you show us the three methods (and the "get-arounds", if they are different)? I'm not sure what you mean by "normal" and "0.00", and even if I did, I might assume a different method than the ones you are objecting to.

I think you have to use a different method for repeating decimals (bar notation), because they can't be written in a terminating form as the others presumably are.

normal decimals are 1.56 or 8.35
0.00 decimals are 0.0999 decimals and such

 

[Dr.Peterson]

We prefer attaching images directly rather than linking to sites with ads; to make these easier to see, I've attached them here:

normal decimals are 1.56 or 8.35
0.00 decimals are 0.0999 decimals and such

I don't see that they've distinguished 1.56 from 0.0999; those are both terminating decimals, and the same basic method is used. There are clearer ways to explain this, beyond expecting you to know already how to "say the name" of a decimal.

For one good explanation, see https://www.mathsisfun.com/converting-decimals-fractions.html.​

There are two cases for repeating decimals, however. They can be combined into one case, and the method you have been shown is rather "magical", putting memorization in place of understanding what is really going on.

For a brief explanation of this (and also of the terminating case), see https://www.purplemath.com/modules/percents2.htm#Decimal_to_Fraction.​

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For a fuller version, see https://brilliant.org/wiki/converting-repeating-decimals-into-fractions/​

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For another, see http://mathforum.org/dr.math/faq/faq.fractions.html#decfrac​