Converting decimal fractions to fractions is very simple. Do you want to learn? Read on!
Method 1 of 2: If the decimal is interrupted
Step 1. Write down the decimal fraction
If the decimal fraction is finite, then it ends one or more decimal places. Let's say we are working with a finite fraction of 0.325. Let's write it down.
Step 2. Let's convert the decimal fraction to a common one
To do this, count the number of decimal places. In our case, there are three digits in the number 0.325. Let's just write the number "325" over the number 1000, which is 1 followed by three zeros. If we were dealing with the number 0.3, with one decimal place, then we would write it as 3/10, or three above, and one with the number of zeros equal to the number of decimal places below.
You can also say the decimal point out loud. In our case, we get 0.325 = "0 whole and 325 thousandths." Sounds like a regular fraction, doesn't it? We write 0.325 = 325/1000
Step 3. Find the greatest common factor of the numerator and denominator of the new fraction
This is how ordinary fractions are simplified. Find the largest number by which both the numerator and the denominator are divisible without a remainder. In our case, this number is 25.
- You don't need to find the greatest common factor right away. You can simplify the fraction and gradually. For example, if we are dealing with two even numbers, we can divide them by 2 until one of them becomes odd or until we simplify to the end. If we are dealing with an even and an odd number, we can try to divide by 3.
- If we are dealing with a number ending in 0 or 5, we will divide by 5.
Step 4. Divide both numbers by the greatest common factor
Divide 325 by 25, we get 13.1000 by 25 = 40. The simplified fraction is 13/40. So 0.325 = 13/40.
Method 2 of 2: If the decimal is periodic
Step 1. Write down the fraction
In a periodic decimal fraction, certain numerical combinations are repeated, it is infinite. For example - 2.345454545. In this case, you need to find x. Write x = 2.345454545.
Step 2. Multiply the number by a power of ten, which would move the non-repeating part of the decimal fraction to the left of the decimal point
In this case, the first degree 10 is enough for us, we write "10x = 23.45454545…." Why do this? If we multiply the right side of the equation by 10, then the left side must also be multiplied.
Step 3. Multiply the equation by another power of 10 to move more digits to the left of the decimal point
For example, let's multiply the decimal fraction by 1000. Let's write, "1000x = 2345.45454545…." This must be done because since we are multiplying the right side of the equation by 10, then the left side must also be multiplied.
Step 4. Let's write a variable and a constant value on top of each other for subtraction
Now let's write the second equation above the first so that 1000x = 2345.45454545 is above 10x = 23.45454545, as it would be with a normal subtraction.
Step 5. Subtract
Subtract 10x from 1000x to get 990x. Then we subtract 23.45454545 from 2345.45454545, we get 2322. We get 990x = 2322.
Step 6. Find x
We know that 990x = 2322, and "x" can be found by dividing both sides by 990. So x = 2322/990.
Step 7. Simplify the common fraction
Divide the numerator and denominator by the common factor. Find the greatest common factor and simplify the fraction completely. In our example, the greatest common divisor of 2322 and 990 is 18, so we divide the numerator and denominator by 18. We get 990/18 = 129 and 2322/18 = 129/55. So 2322/990 = 129/55. Ready!
- Is always check your answer. 2 5/8 = 2.375 - seems to be correct, but if you got 32/1000 = 0.50, then somewhere there is an error.
- Repetition is the mother of learning.