Converting a simple fraction to a decimal number is pretty easy once you understand how it works. You can do this with a simple column division, multiplication or even using a calculator if you prefer. Once you master the technique, you will be able to move from decimal numbers to fractions (and vice versa) with agility.
Steps
Method 1 of 4: With a Column Division
Step 1. Write the denominator outside the division sign and the numerator inside it
Let us consider the fraction 3/4. Simply write "4" outside the division bar and "3" inside. At this point "4" is the divisor and "3" is the dividend.
Step 2. Put a zero with a decimal point above the division bar
Since you are working with a fraction where the numerator is less than the denominator, you know that the corresponding decimal is less than one; for this reason this step is necessary. Now put the comma next to the 3 and write a zero. Although 3 and "3, 0" represent the same value, this step allows you to divide 30 by 4.
Step 3. Proceed to carry out the division by column to find the solution
With this method, you have to pretend that the decimal point after 3 does not exist in order to divide 30 by 4:
- First divide 30 by "4". The closest solution is 7, since 4x7 = 28, leaving a remainder of 2. So write 7 after the "0," you previously noted above the divider. Under "3, 0" write "28". Under these two numbers write 2, your remainder, which is also the difference between 30 and 28.
- Now add another "0" to "3, 0" so you get "3, 00" pretending it's "300". This allows you to lower a zero near "2" and proceed to divide "20" by "4".
- Do the division "20": "4" and you get 5. Write the result to the right of "0, 7" which is above the division bar and you get "0, 75".
Step 4. Write down the solution
Now you have found that "3" divided by "4" is equal to "0.75". This is your answer.
Method 2 of 4: With a Periodic Decimal Number
Step 1. Set up the column division
When you are about to do a split, you may not always know in advance if you will get a periodic number before you start. Let us consider the problem of converting 1/3 to a decimal number. Then write the division into column with the number 3 (the denominator) outside the division bar and 1 (the numerator) inside it.
Step 2. Above the divider bar put a zero followed by the decimal point
Since you already know that the result will be less than one (1 <3) then proceed with this step. You should also do the same after the number "1" and write a comma.
Step 3. Do a column split
Start transforming "1." in "1, 0" so you can think of it as "10". Here's how to proceed:
- Simply divide 10 by 3. You will get that 3x3 = 9 with the remainder of 1. Then write 3 after the "0," which is above the division bar. Subtract 9 from 10 and you get 1, the remainder.
- Add another "0" after "1" (the rest) and you still get "10". When you divide "10" by "3" you enter a repetitive process, from which you will always get a quotient of 3 with a remainder of 1.
- Continue and you will notice that the pattern repeats itself. You could go on indefinitely and continue dividing 10 by 3 to get another 3 (to be added as a decimal figure above the division bar), with a remainder of 1.
Step 4. Write the solution
Now that you noticed that you could write "3" to infinity, write the solution simply as "0, 3" with a hyphen above the "3", indicating that it is a periodic decimal. Alternatively, you can write "0, 33" with the hyphen above both 3. This is the decimal value corresponding to 1/3, but you will never be perfect by ending the sequence of decimal places.
There are many fractions that represent a periodic decimal such as 2/9 ("0, 2" periodic), 5/6 ("0, 83" with "3" periodic), or 7/9 ("0, 7" periodic). This happens whenever you have a multiple of 3 in the denominator and a numerator that cannot be perfectly divided
Method 3 of 4: With Multiplication
Step 1. Find a number that multiplied by the denominator gives a product of 10 or a multiple of it (100, 1000, and so on)
This is a very simple technique for converting a fraction to decimal without using a calculator or doing long divisions in a column. First find the number that multiplied by the denominator gives as a result 10, 100, 1000 and so on, to do this divide 10, 100, 1000 etc.. by the denominator, until you get an integer quotient. Here are some examples:
- 3/5. 10/5 = 2 which is an integer. Now you know that if you multiply 5x2 you get 10, so 2 is your "magic number".
- 3/4. 10/4 = 2, 5 which is not an integer but 100/4 = 25. Now you know that by multiplying 4 x 25 you get 100, so 25 is the number you are interested in.
- 5/16. 10/16 = 0, 625, 100/16 = 6, 25, 1,000 / 16 = 62, 5, 10,000 / 16 = 625, the latter is an integer. If you multiply 16 x 625 you get 10,000, so you have to consider the number 625.
Step 2. Multiply both the numerator and denominator by this “magic number”
It is a simple calculation. Here's what it should look like:
- 3/5 x 2/2 = 6/10
- 3/4 x 25/25 = 75/100
- 5/16 x 625/625 = 3.125 / 10,000
Step 3. The solution you are looking for is equal to the numerator after moving the decimal point to the left by as many zeros as appear in the denominator
At this point, check the denominator and count the zeros it presents. If there is only one zero, move the decimal point to the numerator by one place and so on. Here are some practical examples:
- 3/5 = 6/10 = 0, 6
- 3/4 = 75/100 = 0, 75
- 5/16 = 3, 125/10, 000 = 0, 3125
Method 4 of 4: With the Calculator
Step 1. Divide the numerator by the denominator
Is simple. Just use your calculator to do this. The numerator is the digit at the top and the denominator the digit at the bottom. Considering the fraction 3/4, simply press the key corresponding to the "3" followed by the division sign ("÷ '"), at this point press the 4 and finally the equal sign ("=") and you will get your result.
Step 2. Write the solution
The example above corresponds to 0.75. So the fraction 3/4 corresponds to the decimal number 0.75.
Advice
- To check your result, multiply it by the denominator of the original fraction; the result should be equal to the numerator of the starting fraction.
- Some fractions can be converted into decimal numbers by creating an equivalent fraction that has the denominator with base 10 (10, 100, 1,000, etc). Then place the number so that it results in the correct decimal place.
