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Fraction to Decimal Conversion


The fraction to decimal conversion can be defined as the process of converting a number represented in form of p/q, where p and q belong to whole numbers and q is not equal to 0 into a decimal form by either converting the denominator to a power of 10 or by long division method.

Converting a fraction to a decimal is a straightforward process. Here's a detailed explanation:

Understanding Fractions

A fraction consists of two parts:

- Numerator: The top number, which represents how many parts you have.
- Denominator: The bottom number, which represents how many parts make up a whole.


  • For example, in the fraction 3/4
    ​
    The numerator is 3.
    The denominator is 4.

    Conversion Process

    1. Division Method: The most common method for converting a fraction to a decimal is to divide the numerator by the denominator.
        

To convert a fraction to a decimal, follow the steps given below:

- Take the numerator part as the dividend and the denominator part as the divisor.
- If the dividend is less than the divisor, then add a point and a zero to the dividend.
- Divide the dividend by the divisor.
- Add a "0." to the left of the quotient and express the fraction as a decimal.

    

Example 1: 3/4
Divide 3 by 4:

        3 ÷ 4 = 0.75

    


    3 /4 is equivalent to 0.75 in decimal form.


Example 2: 7/8
    Divide 7 by 8:
    7 ÷ 8 = 0.875
    

    7/8 is equivalent to 0.875 in decimal form.

Example 3: 25/8
    Divide 25 by 8:
    25 ÷ 8 = 3.123
    

    25/8 is equivalent to 3.123in decimal form.


Special Cases

- Terminating Decimals: Some fractions, when converted to decimals, end after a certain number of digits. For example, 1/2 = 0.5
- Repeating Decimals: Some fractions result in a repeating decimal. For example, 1/3 = 0.3333...
    where the 3 repeats indefinitely. This can be written as 0.3 to indicate the repeating part.


Practical Tips
Recognize common fractions and their decimal equivalents for faster calculations (e.g., 1 /2  = 0.5, 1 /4 = 0.25 ).
For repeating decimals, be aware of the notation 0.X to denote the repeating part.


Summary

To convert a fraction to a decimal:


- Divide the numerator by the denominator.
- If the division ends, you have a terminating decimal.
- If the division results in a repeating pattern, you have a repeating decimal.