Convert Between Number Bases

[onesun0000]

Hi Please help. I my teacher gave this as challenge problem in number bases= and I have no idea how to solve this. what we just learned is to convert like 120_5 to base 10. no variables or imaginary or something else as base. sorry i really can't show you a solution because I really don't know how to solve this. I tried searching but I can't find any explanation or at least solution. Thank you.

 

[HallsofIvy]

What do you understand about "bases"? Do you understand that "4328", base 10, means 4*1000+ 3*100+ 2*10+ 8= 4(10^3)+ 3(10^2)+ 2(10^1)+ 8(10^0)?

The first number you are given is \(\displaystyle 4321_i\). I would NOT interpret that "i" as the imaginary unit but simply as some integer (presumably larger than 4). In any case, it is \(\displaystyle 4(i^3)+ 3(i^2)+ 2(i)+ 1\) what ever "i" represents. If "i" is, in fact, the imaginary unit, then that is \(\displaystyle -4i-3+ 2i+ 1= -2i- 2\).

The second is done the same way. The third, \(\displaystyle abc_x\), is \(\displaystyle ax^3+ bx^2+ c\)

 

[pka]

Hi Please help. I my teacher gave this as challenge problem in number bases= and I have no idea how to solve this. what we just learned is to convert like 120_5 to base 10. no variables or imaginary or something else as base. sorry i really can't show you a solution because I really don't know how to solve this. I tried searching but I can't find any explanation or at least solution.
View attachment 10965

I will give you two examples and expect you to post you answer to the above.
\(\displaystyle 2764_{10}=2\cdot 10^3+7\cdot 10^2+6\cdot 10^1+4\cdot 10^0\) that is our everyday number. You should try to understand it.

Here is a base six: \(\displaystyle 51043_{6}=5\cdot 6^4+1\cdot 6^3+0\cdot 6^2+4\cdot 6^1+3\cdot 6^0=6723\) SEE HERE

You post the above assigned problem.

 

[onesun0000]

oh I actually tried once more and what i got is this. and i am struggling to another problem and my answer is at the bottom. I think it's definitely wrong. but i reallty tried my best

 

[pka]

oh I actually tried once more and what i got is this. and i am struggling to another problem and my answer is at the bottom. I think it's definitely wrong. but i reallty tried my best

View attachment 10966

I have no idea whatsoever what the scratching on that paper mean. Why the h are you using \(\displaystyle i~?\) That symbol has a very definite mathematical meaning.
Post a readable question. Do not post an image.
For example: convert \(\displaystyle 13847_{10}\) to base five.

 

[onesun0000]

oh I actually tried once more and what i got is this. and i am struggling to another problem and my answer is at the bottom. I think it's definitely wrong. but i reallty tried my best

View attachment 10966

i already got the additional challenge: that's mnpq to base x

 

[onesun0000]

I have no idea whatsoever what the scratching on that paper mean. Why the h are you using \(\displaystyle i~?\) That symbol has a very definite mathematical meaning.
Post a readable question. Do not post an image.
For example: convert \(\displaystyle 13847_{10}\) to base five.

oh sorry . my bad. . I thank you for your help. really. but I don't feel good about how the tone of your reply kinda make me feel like my mistake will lead to the demise of the world. is it hard to say it lightly? not like you're pouring out your anger to the universe onto me. I appreciated your help but I that's just how I feel about you.

 

[onesun0000]

What do you understand about "bases"? Do you understand that "4328", base 10, means 4*1000+ 3*100+ 2*10+ 8= 4(10^3)+ 3(10^2)+ 2(10^1)+ 8(10^0)?

The first number you are given is \(\displaystyle 4321_i\). I would NOT interpret that "i" as the imaginary unit but simply as some integer (presumably larger than 4). In any case, it is \(\displaystyle 4(i^3)+ 3(i^2)+ 2(i)+ 1\) what ever "i" represents. If "i" is, in fact, the imaginary unit, then that is \(\displaystyle -4i-3+ 2i+ 1= -2i- 2\).

The second is done the same way. The third, \(\displaystyle abc_x\), is \(\displaystyle ax^3+ bx^2+ c\)

Thank you so much. I do understand that. your help really helped me. I will just ask my teacher if what she meant on that "i' is a variable or the imaginary. thank you ...

 

[pka]

oh sorry . my bad. . I thank you for your help. really. but I don't feel good about how the tone of your reply kinda make me feel like my mistake will lead to the demise of the world. is it hard to say it lightly? not like you're pouring out your anger to the universe onto me. I appreciated your help but I that's just how I feel about you.

Please forgive me for giving any reason for you to think that I was capable of “pouring out my anger to the universe”. I do not even believe is such a thing. But it is very simple: I am accustomed to dealing with academically competitive students. Again please forgive me if I misread you.

 

[onesun0000]

Please forgive me for giving any reason for you to think that I was capable of “pouring out my anger to the universe”. I do not even believe is such a thing. But it is very simple: I am accustomed to dealing with academically competitive students. Again please forgive me if I misread you.

I understand what you meant. but for the sake of using the same "i" my teacher used, i intentionally made it that way on my solution. I am not sure whether she used that symbol as the imaginary unit or a variable, but since that symbol is mainly used for imaginary numbers, I think she wanted us to solve it like a numeral in base i (imaginary). so i changed my answer to -i-1 and -2i-1 (with the right symbol for imaginary number) and for the additional challenge question:

Convert (mx^3 + nx^2 + px + q)_10 to base x, I changed my answer to mnpq_x (mnpq to base x).

My apologies for behaving that way, as well. I want to be as kind, respectful as I should be since you all are smart and well-experienced in Math, while in my case, I'm just an average and not-really-good-at-math student. Please bear with us who make a lot of mistakes. We can all be friends and we can help each other, if you let us. A simple kindness when you correct people like us will make us more encouraged. that's that's the goal of this site, I guess. To help you experienced guys to encourage us not-so-well-in-math to do better and learn to the best of our capabilities. thank you again for your help. that really helped me understand what was goin' on with my homework

 

[Harry_the_cat]

What do you understand about "bases"? Do you understand that "4328", base 10, means 4*1000+ 3*100+ 2*10+ 8= 4(10^3)+ 3(10^2)+ 2(10^1)+ 8(10^0)?

The first number you are given is \(\displaystyle 4321_i\). I would NOT interpret that "i" as the imaginary unit but simply as some integer (presumably larger than 4). In any case, it is \(\displaystyle 4(i^3)+ 3(i^2)+ 2(i)+ 1\) what ever "i" represents. If "i" is, in fact, the imaginary unit, then that is \(\displaystyle -4i-3+ 2i+ 1= -2i- 2\).

The second is done the same way. The third, \(\displaystyle abc_x\), is \(\displaystyle ax^3+ bx^2+ c\)

Halls, I think you mean \(\displaystyle ax^2+bx+c\).