Original Post restored

[oztri]

hello, the math problem is "convert 3/8 to a decimal".

the answer is 0.375

I know how to do it with a calculator.

but how do I do it by long division?

this is where i get stuck
3 with a remainder of 12
8/30
-24
60

i get stuck with the answer of 0.3 with some other decimals not .375

thanks in advance for your help

p.s. some tips on how to write a math problem in here would help since i don't know how make a long division symbol

problem solved on my own. cant delete thread

 

[JeffM]

hello, the math problem is "convert 3/8 to a decimal".

the answer is 0.375

I know how to do it with a calculator.

but how do I do it by long division?

this is where i get stuck
3 with a remainder of 12
8/30
-24
60

i get stuck with the answer of 0.3 with some other decimals not .375

thanks in advance for your help

p.s. some tips on how to write a math problem in here would help since i don't know how make a long division symbol

Well you and I are even because I do not know how to write out long division here either. In any case, it is probably not worth your while to learn how to use the rendering software at this site unless you plan to ask a ton of questions.

First, I'll show you WHY $\displaystyle \dfrac{3}{8} = 0.375.$

$\displaystyle 8 * \dfrac{3}{8} = 3.$ Obvious.

$\displaystyle 8 * 0.375 = 8 * 0.3 + 8 * 0.07 + 8 * 0.005 = 2.40 + 0.56 + 0.04 = 3.$

If two numbers when multiplied by 8 are equal, then those two numbers must have been equal in the first place.

OK Let's see how you do this division, taking it step by step (which long division does in a mechanical way so that you do not really see why it works).

$\displaystyle 3.0 \div 8 = 0.3\ with\ remainder\ 0.6.$

But what does a remainder mean anyway. It's just a long way of saying in English what is meant mathematically by

$\displaystyle 3 \div 8 = 0.3 + \dfrac{0.6}{8}.$

But decimal notation does not like a fraction or remainder. So let's divide 0.6 by 8.

$\displaystyle 0.60 \div 8 = 0.07\ with\ remainder\ 0.04.$

Which means that $\displaystyle 3 \div 8 = 0.3 + 0.07\ with\ remainder\ 0.04 = 0.37\ with\ remainder\ 0.04 = 0.37 + \dfrac{0.04}{8}.$

But decimal notation does not like a fraction or remainder. So let's divide 0.04 by 8.

$\displaystyle 0.040 \div 8 = 0.005\ with\ no\ remainder\ and\ so\ no\ fraction.$

Which means that $\displaystyle 3 \div 8 = 0.37 + 0.005 = 0.375.$

Does that help?

 

[oztri]

thanks for your help JeffM, greatly appreciated

 

[MarkFL]

You can also write:

$\displaystyle \displaystyle 0.375=\frac{375}{1000}=\frac{3\cdot125}{8\cdot125}=\frac{3}{8}$

 

[oztri]

thanks Markfl.

 

[lookagain]

hello, the math problem is "convert 3/8 to a decimal".

the answer is 0.375

I know how to do it with a calculator.

but how do I do it by long division?

this is where i get stuck
3 with a remainder of 12
8/30
-24
60

i get stuck with the answer of 0.3 with some other decimals not .375

thanks in advance for your help

p.s. some tips on how to write a math problem in here would help since i don't know how make a long division symbol

$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0. \ 3 \ 7 \ 5$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$|--------
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ 8 \ \$$\displaystyle | \ \ 3. \ 0 \ 0 \ 0$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ 4$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$-----
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6 \ 0$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5 \ 6$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$-----
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4 \ 0$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4 \ 0$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ -----
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0 \ \ \ \ \ Remainder$



To show the long division, I used some Latex I knew and "macgyvered it."

 

[oztri]

your formating looks good lookagain. thanks

 

[lookagain]

That line is 2 -'s too long

I disagree, Denis. I felt that line was three of those characters too long,
so I deleted three of them.