How Does Long Division Explain 1 Divided by 2 Equals 0.5?

[physio]

I understood the logic behind long division which many teachers don't make any student understand! For example if I have 1506/2 then 1506 can be written as 1000+500+00+6 and then we can determine how many 'twos' are there in 1000,500,00 and 6. That gives us an answer of 500+250+0+3=753.

1) Now, what I don't understand is how do we get 0.5 using the long division method when we divide 1 by 2?

2) How does the decimal system work in long division??

 

[coolul007]

One uses the rule of decimal point placement, in actuality it's a hidden powers of ten notation. By allowing a decimal point for every number, whether we write it or not(mainly whole numbers much like the plus sign for positive numbers), then applying the rules, we get a decimal expansion.

 

[chingel]

if 1/2=x then multiplying both sides by 10, 10/2=10x, which you calculate out to get 10x. To get x, you divide by 10. So you can add a zero to the number being divided if you remove a zero, (ie shift the comma), from the answer.