How do I write a decimal as a fraction or mixed number in simplest form

Question

mathstudent55 · Answer

If the decimal number terminates (it ends, doesn't go on for ever), then just read the number and write a fraction. Then reduce the fraction, if possible.
For example:
Write 0.475 as a fraction
0.475 is read as four hundred seventy-five thousandths, so write
$$\frac{ 475 }{ 1000 }$$
Now reduce, 475/1000 = 19/40

mathstudent55 · Answer

If the number is a non-terminating, repeating decimal (a number that doesn't end but a pattern repeats), then it can be written as a fraction.
Example: Write 0.33333333... as a fraction
First step: How many digits repeat? only one, the 3
Start with x = 0.333...   (Eq. 1)
Since only one digit repeats, now multiply both sides of above equation by 10 (1 followed by 1 zero, 1 zero bec only one digit repeats.)
10x = 3.3333...   (Eq. 2)

Now write Eq. 2 above Eq. 1 and subtract Eq. 1 from Eq. 2:

10x = 3.33333....
    x = 0.33333....
----------------
 9x  = 3
Solve for x:
x = 3/9 = 1/3
So 0.333... = 1/3

mathstudent55 · Answer

Example with 2 repeating decimals:
Write 0.818181... as a fraction
      x = 0.818181...

Here you multiply by 100 (1 followed by TWO zeros bec 0.818181... has TWO digits repeating)
100x = 81.818181...
      x =  0.818181...
Subtract:
99x = 81
x = 81/99 
x = 9/11
So 0.818181... = 9/11