In the previous articles, we have various details regarding all the fractions such as like and unlike fractions, equivalent fractions, etc. Check the conversion of fractions here along with the formulae and methods. Refer to all the steps to convert decimal to fractions as well as fractions to decimals. The detailed process for the conversion of fractions is given here. Go through the below sections to know the rules, methods, and formulae, etc.
Conversion of Fractions – Introduction
Conversion of the fractions involves various steps. Each step is explained in detail here. We are providing the complete guide to converting fractions to decimals and also decimals to fractions.
How to Convert Decimals to Fractions?
To convert the decimals to fractions, we have a process to follow. Below are the steps to convert decimals to fractions.
- Note the decimal fraction number as a fraction of the digits number to the right of the numerator i.e., decimal period and denominator to the power of 10.
- Find the GCD (greatest common divisor) of the denominator and the numerator.
- Now, reduce the fraction value by dividing the denominator and numerator with the greatest common divisor.
Converting a Terminal Decimal to a Fraction
Terminating decimals are any decimal numbers which has finite digits. In other words, terminating decimal has an end.
Examples:Â
0.5,0.234,0.864721 etc.
These decimals are the common decimals you will see and they are the easiest way to convert to fractions.
Step 1:
Write the decimal in the form divided by one.
For suppose, you have the decimal number 0.5. Your first step is to write out the decimal. Hence, it looks like 0.5/1
Step 2:
In the next step, you have to multiply both the bottom and top of the new fraction by 10 to all the digits that are at the left of the decimal point.
For suppose, 0.55 is the decimal fraction. In the given fraction, 0.55 has two digits after the decimal point. Therefore, we have to multiply the entire equation by 10 * 10, or 100. If we multiply the fraction with 100/100 gives the result 55/100
Step 3:
The last step is to reduce the fraction to its simplest form.
Suppose that 0.5 is the number, then to denote the fraction value we write it as 5/10 = 1/2. For the number 0.15, we write it as 15/100. Then the result will be 3/20.
Note:
Use the last digits place value to define the fraction with a denominator of 10,100,1000 etc. Then try for further simplification to get the exact result value.
Converting a Fraction into a Decimal
To convert the fraction values into a decimal value, there are certain steps to be followed.
Step 1:
First of all, change the given fraction value into equivalent fraction values with denominators 10,100,1000, etc.
Suppose that 3/4 is a fraction value. Now, divide the denominator value i.e., 3/4 by 25, so that the value becomes 75/100. We have to concentrate on changing the decimal value to an equivalent fraction.
Step 2:
Multiply both numerator and denominator by that number.
Suppose that 3/4 is a fraction value. Now, divide the denominator value i.e., 3/4 by 25, so that the value becomes 75/100. We have to concentrate on changing the decimal value to an equivalent fraction.
Step 3:
Take the count of no of zeros in the denominator after the 1st digit. Now, put the decimal point in the numerator, starting from the extreme of right, and then move that decimal point to the left and equal the number of zeros.
Converting Fractions to Recurring Decimals
In some of the cases, conversion of fraction value leads to the result of repeating decimal value i.e., the same decimal value recurs forever throughout the similar number pattern.
Example:
Consider 2/3 as the fraction value, to convert the fraction value into the decimal value. First, divide the numerator value 2 by the denominator value 3. To continue the process of division, we have to add trailing zeros to the number 2.
Therefore, we can notice that the division continues, no matter the number of trailing zeros you add to the number 2. In this case, 2/3 = 0.6666….
In the above example, the bar is placed above the repeating integers to define that the number recurs forever.
There is also another case where more than 1 integer recurs in the decimal number either by alternating or consecutively.
Example:
Suppose that you have to convert the fraction value 5/11 to the decimal fraction. First, divide the numerator value 5 by the denominator value 11. To continue the process of division, we have to add trailing zeros to the number 5.
We can notice that the pattern of division repeats every integer 4 and 5. If we add trailing zeros to the original decimal value, then the string out the pattern indefinitely. The final result can be written as 0.45454545…..
Conversion of Fraction Value to Decimal Value when the denominator is a Multiple of 10
Whenever the denominator value of a fraction is the multiple of 10 i.e., 10,100,1000,10000, etc. Then conversion of a fraction value to a decimal value is a straightforward process.
First, the total number of zeros present in the denominator are counted, and then the numerator is written down
When the denominator of a fraction value is a multiple of 10, 100, 1000, 10000, etc. Then conversion of the fraction value to a decimal value is a straightforward process. The numerator is written by placing the decimal point before the number where a number of zeros are present from right to left.
Example:
Suppose 25/100 is a fraction value.
To convert the value 25/100 into a decimal value
We have to check for the number of zeros in the denominator, Hence the denominator value is 100, there are 2 zeros present in the denominator. Therefore, we have to shift the decimal point by 2 points in the numerator. Then the final result is 0.25
Example 2:
Suppose 276/1000 is a fraction value.
To convert the value 276/1000 into a decimal value.
We have to check for the number of zeros in the denominator, Hence the denominator value is 1000, there are 3 zeros present in the denominator. Therefore, we have to shift the decimal point by 3 points in the numerator. Then the final result is 0.276
Conversion by long division method
Conversion of the fraction value to decimal value by using the long division method involves various steps. The steps to be followed are:
Step 1:
In the first step, we convert the dividend value to the most suitable equivalent decimal value.
Whenever the digit to the right of the decimal value is bought down, we have to insert the decimal point in the quotient.
Example: Convert 3/4 into decimals.
Solution:
As already given 3/4 is the fractional value. Here 3 has to be divided by 4. As 3 is less than 4, it cannot be f=divided by 4
Therefore, we can write the value as 3.00 which can be divided by 4.
30 can be divided by 4 for 7 times. Therefore we write the quotient as 0.7, on further division, we get the final result as 0.75