how to you turn a decimal into a fraction

Question

how to you turn a decimal in to a fraction..ex 215.1111111111

Answer 1

Nicole

 

To convert a decimal with a repeating digit to a fraction

Take your original number and multiply it by 10

 

in your case we have

x = 215.1111111111

now if we multiply it by 10

10x = 2151.111111111

 

Now we have two numbers with the same repeating decimal parts.

What if we subtracted these two equations ?

10x = 2151.1111111111
-  x = -215.1111111111
-------------
9x = 1936.

The reason for doing this is notice how all of the repeating decimal parts have subtracted away to zero! We are left with a nice, simple 1936 on the right side of the equal sign.

Now, solving 9x=1936 for x by dividing both sides of it by 9, we'll get that x=1936/9. And this is your answer.

to verify enter 1936/9 into calculator, you should get 215.1111111111

Do note that this fraction x = 1936/9 is an improper faction - the numerator is greater than the denominator. Although there is nothing wrong with this, one usually simplifies an improper fraction into a mixed number.

 

The whole number part of the mixed number is found by dividing the 1936 by the 9.
In this case we get 215.

The fractional part of the mixed number is found by using the remainder of the division,
which in this case is 1 (1936 divided by 9 is 215 remainder 1).


So your final answer is: 215.111111 can be written as the fraction 215 1/9

 

Do note you could have automatically pulled out the whole number 215 from your original number 

 215.1111111111 and then have done the steps above using only y =  0.1111111111

 

y = 0.1111111111

10y = 1.1111111111

 

10y =  1.1111111111

-  y = -0.1111111111

-------------

9y = 1

 

y = 1/9

 

answer is 215 + 1/9 = 215 1/9

 

more explanations and examples can be found at purple math

http://www.purplemath.com/modules/percents.htm

 

good luck

Answer 2

Hi Nicole,

let me use your example.

 

215.111111111 = 215.111111111 

                                        1

the rule is to multiply numerator and denominator by 10ⁿ where n is the number of digits following the decimal point.

In this case you have 9 digits after the decimal point (that is nine 1), so you have to multiply by 10⁹ both the numerator and the denominator.

 

215.111111111 x 10⁹   ₌ 215111111111

           1x10⁹                          1000000000

 

In this case it's hard to simplify the fraction!

 

 

 

Answer 3

Hi Nicole! To convert a decimal to a fraction, follow these steps:

 
1. Write down the decimal divided by 1. Take the example 2.25:

       2.25

         1

 

2. Convert both the numerator (top) and denominator (bottom) into whole numbers. This is done by multiplying both the numerator and denominator by 10 for each digit to the right of the decimal point in the numerator. In the case of 2.25, there are 2 digits after the decimal point, so we multiply both the 2.25 and the 1 by 10 x 10 (which is 100):
 
        225
        100

 
3. Simplify the fraction. In the case of 225/100, you can simplify easily in 2 steps:

 

       225 divided by 5 = 45      45 divided by 5 = 9

       100 divided by 5 = 20      20 divided by 5 = 4

  
So, the fraction equivalent of 2.25 is 9/4. Hope that helps!

 
Bill