Calculator help

[RESmonkey]

Ok, so I put an fnInt problem in my calc, and got 17.3333333333... as an answer. I wanted it in a fraction, so I did MATH > FRAC. It didn't convert, and just outputted the decimal again.

I manually typed 17.333333333 (same decimal count) and tried it, and it rounded.

Why aren't my answers being rounded right away?

This has happened twice so far with the current homework assignment, all using fnInt().


edit = It's a Ti-84 Silver Edition.

edit = Clifs:

My calculator doesn't convert answers to fractions. (decimal answers outputted from fnInt() ).

 

[KillerCharlie]

That's because you're integrating numerically, and your output is a NUMERICAL solution, not an analytical solution. The calculator has no idea that it's 17+1/3 - it just calculated 17.3333333333. It doesn't know that the 3 repeats forever.

As to why it rounded when you typed in 17.333333, I'm not sure - I think it's stupid since what you entered is a finite decimal, NOT 17+1/3.

You're getting confused by the difference between rounding a number of a fraction and converting a repeating decimal to a fraction.

From what I recall, a Ti-83 does all integration numerically. The Ti-89 integration first attempts to integrate analytically, then tries to integrate numerically. Sometimes it will give you, for example, "pi" if finds an analytical solution, or 3.14159... if it doesn't.

 

[RESmonkey]

Yeah, it managed to round the very same decimal that I typed in and convert to frac. Heh.

Oh well

thanks

 

[DrPizza]

Because your calculator stores the value to more decimal places than you see on the screen. And, on such calculations, there are often rounding errors present. If you repeat the calculation, and subtract 17.33333333, you may discover that what's left is something like 3333548E-09

 

[jlee]

Originally posted by: DrPizza
Because your calculator stores the value to more decimal places than you see on the screen. And, on such calculations, there are often rounding errors present. If you repeat the calculation, and subtract 17.33333333, you may discover that what's left is something like 3333548E-09

:thumbsup:

I imagine the calculator is running x.333[...]until it runs out of available numbers in memory (or however it works..), regardless of what's displayed on the screen.

 

[frostedflakes]

Bingo, it calculates it to many more digits, just doesn't display them all. If it can't convert the number to a fraction it's irrational.

 

[DrPizza]

Incidentally, I absolutely hate calculators - they've caused us to have a whole generation of kids with minimal knowledge of the most basic of mathematics. One has to question how well they actually understand mathematics when they lack the ability to do these most basic things in their heads. It's akin to being able to write a paragraph in a foreign language, but having no idea what any of the words are.

Seriously, you had 17.33333333... on a calculator and actually bothered to hit the decimal -> frac??! *sigh* I guess it isn't as bad as the girl I was tutoring last week who couldn't do 6*8 without a calculator.

 

[RESmonkey]

Originally posted by: DrPizza
Incidentally, I absolutely hate calculators - they've caused us to have a whole generation of kids with minimal knowledge of the most basic of mathematics. One has to question how well they actually understand mathematics when they lack the ability to do these most basic things in their heads. It's akin to being able to write a paragraph in a foreign language, but having no idea what any of the words are.

Seriously, you had 17.33333333... on a calculator and actually bothered to hit the decimal -> frac??! *sigh* I guess it isn't as bad as the girl I was tutoring last week who couldn't do 6*8 without a calculator.

Dude, chill. I know it's seventeen plus a third. I wanted a improper fraction, because it was a multiple choice question (AP).

 

[frostedflakes]

Come on have some faith in us, I'm sure RES knows how to convert decimals to fractions. I tend to use >FRAC a lot because it's faster for most numbers (obviously stuff like 1.5 or 1.33 jumps out at you immediately) and prevents me from making stupid arithmetic errors.

 

[RESmonkey]

Originally posted by: frostedflakes
Have some faith in us kids, I'm sure RES knows how to convert decimals to fractions. I tend to use >FRAC a lot because it's faster for most numbers (obviously stuff like 1.5 or 1.33 jumps out at you immediately) and prevents me from making stupid arithmetic errors.

Yep.

 

[jagec]

'cause fractions suck! NOTHING is known to that degree of precision anyway.

 

[Fenixgoon]

Originally posted by: RESmonkey

Originally posted by: DrPizza
Incidentally, I absolutely hate calculators - they've caused us to have a whole generation of kids with minimal knowledge of the most basic of mathematics. One has to question how well they actually understand mathematics when they lack the ability to do these most basic things in their heads. It's akin to being able to write a paragraph in a foreign language, but having no idea what any of the words are.

Seriously, you had 17.33333333... on a calculator and actually bothered to hit the decimal -> frac??! *sigh* I guess it isn't as bad as the girl I was tutoring last week who couldn't do 6*8 without a calculator.

Dude, chill. I know it's seventeen plus a third. I wanted a mixed fraction, because it was a multiple choice question (AP).

so if the answer is 17 + 1/3, why couldnt you automatically see that 17.33333 = 17 +1/3?

edit: small fractions should be obvious except for anything in 7ths.

 

[frostedflakes]

Because it's actually 17*3 over 3 plus 1/3. Of course 17*3 isn't too difficult if you look at it the right way, 3*20 is 60 minus 3*3 is nine so 51. 51/3 + 1/3 = 52/3.

Or just take a second and press the FRAC button. I'll do this crap in my head for HW problems but on tests I never do because I'm so afraid of making stupid little mistakes. It's also handy for simplifying fractions as well.

 

[jlee]

Originally posted by: frostedflakes
Because it's actually 17*3 over 3 plus 1/3. Of course 17*3 isn't too difficult if you look at it the right way, 3*20 is 60 minus 3*3 is nine so 51. 51/3 + 1/3 = 52/3.

Or just take a second and press the FRAC button. I'll do this crap in my head for HW problems but on tests I never do because I'm so afraid of making stupid little mistakes. It's also handy for simplifying fractions as well.

17*3 is 30 plus 21..



Interesting how different people run things in their head different ways.

 

[RESmonkey]

Originally posted by: Fenixgoon

Originally posted by: RESmonkey

Originally posted by: DrPizza
Incidentally, I absolutely hate calculators - they've caused us to have a whole generation of kids with minimal knowledge of the most basic of mathematics. One has to question how well they actually understand mathematics when they lack the ability to do these most basic things in their heads. It's akin to being able to write a paragraph in a foreign language, but having no idea what any of the words are.

Seriously, you had 17.33333333... on a calculator and actually bothered to hit the decimal -> frac??! *sigh* I guess it isn't as bad as the girl I was tutoring last week who couldn't do 6*8 without a calculator.

Dude, chill. I know it's seventeen plus a third. I wanted a mixed fraction, because it was a multiple choice question (AP).

so if the answer is 17 + 1/3, why couldnt you automatically see that 17.33333 = 17 +1/3?

edit: small fractions should be obvious except for anything in 7ths.

My bad, I meant "improper" fractions.

 

[jagec]

Originally posted by: frostedflakes
Because it's actually 17*3 over 3 plus 1/3. Of course 17*3 isn't too difficult if you look at it the right way, 3*20 is 60 minus 3*3 is nine so 51. 51/3 + 1/3 = 52/3.

Or just take a second and press the FRAC button. I'll do this crap in my head for HW problems but on tests I never do because I'm so afraid of making stupid little mistakes. It's also handy for simplifying fractions as well.

One of the answers was (17*3)/3 + 1/3? That's moronic.

 

[frostedflakes]

Eh? That's standard procedure for adding fractions, you need a common denominator. It doesn't matter how moronic you think it sounds, that's how you get from 17.333 to 52/3.

 

[jagec]

Originally posted by: frostedflakes
Eh? That's standard procedure for adding fractions, you need a common denominator. It doesn't matter how moronic you think it sounds, that's how you get from 17.333 to 52/3.

Exactly, that's just a step in the procedure. Answers should be in reduced form, not a long string of numbers barfed onto the page. I shouldn't see something like:

a) (17/3)/3 + 1/3
b)ln(e^(1+5))/43 + (1+x)/(3x+3)
c) 572/(29 - 2!) *(1+10^(-3/4))

etc.

 

[DrPizza]

Originally posted by: RESmonkey

Originally posted by: DrPizza
Incidentally, I absolutely hate calculators - they've caused us to have a whole generation of kids with minimal knowledge of the most basic of mathematics. One has to question how well they actually understand mathematics when they lack the ability to do these most basic things in their heads. It's akin to being able to write a paragraph in a foreign language, but having no idea what any of the words are.

Seriously, you had 17.33333333... on a calculator and actually bothered to hit the decimal -> frac??! *sigh* I guess it isn't as bad as the girl I was tutoring last week who couldn't do 6*8 without a calculator.

Dude, chill. I know it's seventeen plus a third. I wanted a improper fraction, because it was a multiple choice question (AP).

*sigh* I hope you're joking, because that's equally pathetic. You're in AP calculus and you can't "instantly" convert that to an improper fraction?? I'm not really making fun of you in particular - it's not your fault. There's a whole generation of people like you who are absolutely calculator dependent for the most trivial calculations.