Converting Equations to Binary & Irrational Numbers

In summary, the conversation discusses the conversion of equations and numbers between different number systems, specifically binary and decimal. There is a discussion about the representation of irrational numbers in different number systems and the use of terminology in mathematics. The conversation also touches on the challenges of teaching and discussing numbers systems in a practical setting.
  • #1
jobyts
227
64
... can we convert this equation to binary notation?

Also another one, would an irrational number be irrational in any number format?
 
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  • #2
[tex] 0.999 = 1 [/tex]

Use the standard algorithms to convert [tex] 0.\overline{000} [/tex] to decimal form (do the same for [tex] 1 [/tex], but that isn't as exciting). The results will look different, but if two symbols represent the same quantity in one number system, the corresponding symbols represent the same quantity in any number system.

If you convert (say) [tex] \sqrt 2 [/tex] to another base, you won't get a decimal form, since decimal refers to base 10 alone. You will get a representation, in that other base, of a number that we refer to as irrational in base 10.
 
  • #3
In binary it would be [itex]0.\overline{1111}= 1[/itex] and, yes, it is true.

statdad, while incorrect, there just isn't any good term to replace "decimal fraction" in another base so I would cut jobytx some slack on that.

jobytx, the distinction between "rational" and "irrational" is a property of numbers not numerals and has nothing to do with whether it is represented in base 2 or base 10 or even Roman numerals (although I confess I don't know how one would represent a non-integer in Roman numerals!).
 
  • #4
HallsofIvy;
I agree (I think, unless you are saying my comment is incorrect) with you - language is awkward with this stuff. Here's my reason for the comment.
I'm currently teaching an applied course for folk majoring in computer areas (programming, mostly) and we discuss number systems for our CIS colleagues. They have (for their own reasons) specifically asked us not to refer to "decimal" when using other number systems, whatever the base: they prefer we refer to them as "non-integers", or "representations of decimals".
Think too long and hard like that and it seeps outside the classroom.

If it seems I was being harsh to the OP, I do apologize - that was not my intent.
 
  • #5
statdad said:
HallsofIvy;
I agree (I think, unless you are saying my comment is incorrect) with you
Would I dare say that you are incorrect?

- language is awkward with this stuff. Here's my reason for the comment.
I'm currently teaching an applied course for folk majoring in computer areas (programming, mostly) and we discuss number systems for our CIS colleagues. They have (for their own reasons) specifically asked us not to refer to "decimal" when using other number systems, whatever the base: they prefer we refer to them as "non-integers", or "representations of decimals".
Think too long and hard like that and it seeps outside the classroom.

If it seems I was being harsh to the OP, I do apologize - that was not my intent.
 
  • #6
It's happened many, many, times in my graduate career and in my careers since finishing my degrees. So, if my comment(s) above were in error, let me know. :D

I expect no lower level of honesty from you.
 
  • #7
I agree with you completely. In fact, I dislike the term "decimal fraction" even when working in base 10.

Also, I just noticed that jobyts did not use the term "decimal" himself so you were just giving additional information, not criticizing, and my remark was off base!
 

Related to Converting Equations to Binary & Irrational Numbers

1. How do you convert a decimal number to binary?

To convert a decimal number to binary, you can use the division method. Divide the decimal number by 2 and write down the remainder. Then, take the quotient and divide it by 2 again, writing down the remainder. Continue this process until the quotient is 0. The binary number will be the remainders written in reverse order.

2. What is the significance of converting equations to binary?

Converting equations to binary allows for the representation of numbers in a computer's binary system, which is essential for digital devices to process and store data. It also allows for more efficient computation and communication between devices.

3. How do you convert a binary number to a decimal number?

To convert a binary number to a decimal number, you can use the positional notation method. Starting from the right, each digit in the binary number is multiplied by 2 raised to the corresponding power of its position. The resulting values are then added together to get the decimal equivalent.

4. What is the process of converting irrational numbers to binary?

Converting irrational numbers to binary can be done using the same division method as for converting decimals. However, since irrational numbers have infinite decimal places, the process will continue indefinitely, resulting in an infinite binary number. Therefore, irrational numbers are usually rounded to a certain number of binary places.

5. Why is it important to represent numbers in binary form?

Representing numbers in binary form is important because it allows for efficient processing and storage of data in digital devices. Binary is the basic language of computers, and all information is ultimately represented in binary form for the computer to understand and process.

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