Converting a decimal number to a fraction isn't as difficult as it may seem. If you need to find out how to proceed, simply continue reading this article. If, on the other hand, you need to convert a fraction to a decimal number, read this article. Both methods described may be difficult at first, but remember that practice makes perfect.
Steps
Method 1 of 2: Convert a Finished Decimal Number
Step 1. Make a note of the decimal number to convert
If you need to convert a finite decimal number, it means that it will consist of a specific number of decimal places. Imagine that you need to convert the decimal number 0, 325 into a fraction. Make a note of that value.
Step 2. Convert the decimal number to a fraction
To perform this step, start by counting the digits after the decimal separator. The number 0, 325 is made up of three decimal places. At this point, report the value "325" as the numerator of the fraction and the value 1.000 as the denominator. If you had to convert the decimal number 0, 3, consisting of a single decimal digit, into a fraction, you would have had to represent it with the fraction 3/10.
If you prefer, you can express the final result in literal form. In the example, the decimal number 0, 325 corresponds to "325 thousandths". Even so you are indicating a fraction, since 0, 325 is equal to 325 / 1,000
Step 3. Find the greatest common multiple of the numerator and denominator of the fraction you got as a result of the conversion
This way you can simplify the final result. You will need to find the largest number that can be used as a divisor of both the numerator of the fraction, which is 325, and the denominator, which is 1,000. In this specific case, the greatest common multiple is represented by the number 25, since it is the largest divisor that produces an integer as a result.
- To simplify the fraction you are not obliged to identify the greatest common multiple. If you prefer, you can take a more practical approach and try it out. For example, if you need to simplify a fraction made up of two even numbers, keep dividing them both by 2 until you get an odd number or you can no longer simplify the fraction any further. If you need to simplify a fraction made up of odd numbers, try dividing them by 3.
- If the fraction under consideration is made up of numbers ending in 0 or 5, divide them by the number 5.
Step 4. To simplify the fraction, divide the numerator and denominator by the greatest common multiple you found
Divide the number 325 by 25 to get 13, then divide 1,000 by 25 to get 40. The final result of the conversion will then be 13/40. At this point, you can say that 0, 325 = 13/40.
Method 2 of 2: Convert a Periodic Decimal Number
Step 1. Make a note of the number to convert
A periodic decimal number is made up of a sequence of decimal digits that is repeated indefinitely. For example, the number 2, 345454545 is a periodic decimal number. In this case, set the equation x = 2, 345454545 and solve it for "x".
Step 2. Multiply the number to convert by the power of ten needed to shift all non-repeating decimal places to the left of the decimal point
In the example, it is sufficient to use a single power of 10 obtaining as a result "10x = 23, 45454545….", Since the only decimal digit that does not repeat is 3. The starting equation has taken the form indicated, because if you multiply a member by 10 you must necessarily perform the same operation for the other member as well.
Step 3. Multiply both sides of the equation by another power of 10 to move more digits from the decimal part to the integer part of the number to convert
In this case, assume that you multiply the starting decimal number by 1,000 to get the following equation "1.000x = 2.345, 45454545….". The starting equation has taken the form indicated because if you multiply one member by 1,000 you must necessarily perform the same operation for the other member as well.
Step 4. Column the two equations you have obtained so that the left and right members are aligned with each other
This way, you will be able to subtract the respective values. In the example above, place the second equation above the first, i.e. 1.000x = 2.345, 45454545 above 10x = 23, 45454545 so that you can easily perform the subtraction.
Step 5. Perform the calculations
Subtract the 10x value from 1.000x to get 990x, then subtract the number 23, 45454545 from 2.345, 45454545 to get the value 2.322. The final equation is 990x = 2.322.
Step 6. Solve the equation based on the variable "x"
At this point, solve the equation 990x = 2.322 for the variable "x" by dividing both sides by the number 990. This way, you get x = 2.322 / 990.
Step 7. Simplify the fraction you got
Divide the numerator and denominator by any of the common factors. Find the greatest common divisor of the numerator and denominator of the fraction you got as a result. Continuing with the previous example, the greatest common divisor of 2.322 and 990 is 18, so dividing 990 and 2.322 by 18 you will get 990/18 = 129 and 2.322 / 18 = 55. At this point, the final result of the conversion is equal to fraction 129/55.
Advice
- Remember that practice makes perfect.
- When you have mastered the method to use, solving this type of math problem will only take a few seconds unless you have to simplify the final result you will get.
- If this is your first time doing this type of conversion, it would be better to have a sheet of paper on which you can write notes and partial results and an eraser.
- Check it out always that the result of your work is correct. The equation 2 5/8 = 2.375 seems correct. Conversely, if as a final result you get the following equation 32 / 1,000 = 0.50, it is clear that you have made some calculation errors.
