Converting a decimal to a fractional form is not as difficult as it seems. If you want to know how to do it, follow these steps.
Step
Method 1 of 2: For Non-Recurring Decimals
Step 1. Write down the decimal
If the decimal is not repeating, then there is only one or more numbers after the decimal point. For example, you use the non-repeating decimal 0, 325. Write it down.
Step 2. Convert the decimal to a fraction
To do this, count the number of digits after the decimal point. At 0, 325, there are 3 numbers after the decimal point. So, put the number "325" above the number 1000, which is actually a 1 with 3 0's after it. If you use the number 0, 3, which is only 1 digit after the decimal point, you can change it to 3/10.
You can also say the decimal out loud. In this case 0, 325 = "325 per thousand". Sounds like shards! Write down 0, 325 = 325/1000
Step 3. Find the greatest common factor (GCF) of the new fraction's numerator and denominator
Here's how to simplify fractions. Find the largest number that can divide 325 and 1000. In this case, the GCF of both is 25 because 25 is the largest number that can divide both numbers.
- You don't have to immediately look for FPB. You can use trial and error to simplify the fraction. For example, if you have 2 even numbers, keep dividing them by 2 until one of them becomes an odd number or cannot be simplified. If you have both an odd and an even number, try dividing by 3.
- If you have a number that ends in 0 or 5, divide it by 5.
Step 4. Divide both numbers by the GCF to simplify the fraction
Divide 325 by 25 to get 13 and divide 1000 by 25 to get 40. A simple fraction is 13/40. So 0, 325 = 13/40.
Method 2 of 2: For Repeating Decimals
Step 1. Write it down
A repeating decimal is a decimal that has a never-ending repeating pattern. For example, 2,345454545 is a repeating decimal. This time, we will solve it using x. Write down x = 2, 345454545.
Step 2. Multiply the number by a multiple of ten so that it will move the repeating part of the decimal number to the left of the decimal point
For example, multiplying by 10 is sufficient, so write "10x = 23, 45454545…." You have to do this because if you multiply the right side of the equation by 10, you must also multiply the left side of the equation by 10.
Step 3. Multiply the equation by another multiple of 10 to move more numbers to the left of the decimal point
In this example, multiply the decimal by 1000. Write, 1000x = 2345, 45454545…. You have to do this because if you multiply the right side of the equation by 1000, you must also multiply the left side of the equation by 1000.
Step 4. Put variables and constants on the same side
This is done to make a reduction. Now, put the second equation above so that 1000x = 2345, 45454545 is above 10x = 23, 45454545 is the same as regular subtraction.
Step 5. Subtract
Subtract 10x from 1000x to get 990x and subtract 23, 45454545 from 2345, 45454545 to get 2322. Now you have 990x = 2322.
Step 6. Find the value of x
Now that you have 990x = 2322, you can find the value of "x" by dividing both sides by 990. So, x = 2322/990.
Step 7. Simplify fractions
Divide the numerator and denominator by the same common factor. Use the GCF on both the numerator and denominator to make sure the fraction is at its simplest. In this example, the GCF of 2322 and 990 is 18, so you can divide 990 and 2322 by 18 to simplify the numerator and denominator of the fraction. 990/18 = 129 and 2322/18 = 129/55. Thus, 2322/990 = 129/55. You have done.
Tips
- Practice makes you smoother.
- The first time you use this method, a clean sheet of scrap paper and an eraser are recommended.
- Always check your final answer. 2 5/8 = 2, 375 seems correct. But if you get the value 32/1000 = 0.50, then something is wrong.
- Once you're fluent, these questions can be solved in 10 seconds unless you need to simplify.
