# Decimal to Fraction Calculator

> Convert a decimal number into a simplified fraction instantly. Perfect for math students and professionals.

**Category:** Math
**Keywords:** decimal, fraction, conversion, math, simplify
**URL:** https://complete.tools/decimal-to-fraction

## How it calculates

To convert a decimal (d) to a fraction, the formula used is: 

Fraction = d × (10^n) / (10^n), 

where 'd' is the decimal number, and 'n' is the number of digits after the decimal point. For example, if d = 0.75, there are two digits after the decimal point, so n = 2. The calculation becomes: 

Fraction = 0.75 × (10^2) / (10^2) = 75 / 100. 

Next, to simplify the fraction, find the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 75 and 100 is 25. Thus, dividing both the numerator and denominator by 25 gives: 

75 ÷ 25 / 100 ÷ 25 = 3/4. 

Hence, the decimal 0.75 is equivalent to the simplified fraction 3/4.

## Who should use this

This tool can be particularly useful for: 
1. Home cooks adjusting ingredient measurements from decimal-based recipes. 
2. Engineers performing calculations that require precise fractional values for material specifications. 
3. Students in mathematics courses needing to convert decimals to fractions for homework or exams. 
4. Financial analysts working with percentages and needing to express them as fractions for clearer data representation.

## Worked examples

Example 1: Convert 0.6 to a fraction. 
Step 1: Identify the decimal: d = 0.6. There is one digit after the decimal point, so n = 1. 
Step 2: Apply the formula: Fraction = 0.6 × (10^1) / (10^1) = 6/10. 
Step 3: Simplify by finding the GCD of 6 and 10, which is 2. Divide both by 2: 6 ÷ 2 / 10 ÷ 2 = 3/5. 
Thus, 0.6 equals the simplified fraction 3/5. 

Example 2: Convert 1.25 to a fraction. 
Step 1: d = 1.25, and there are two digits after the decimal, so n = 2. 
Step 2: Fraction = 1.25 × (10^2) / (10^2) = 125/100. 
Step 3: The GCD of 125 and 100 is 25. Divide both by 25: 125 ÷ 25 / 100 ÷ 25 = 5/4. 
Thus, 1.25 equals the simplified fraction 5/4.

## Limitations

The tool has several limitations, including: 
1. Precision Limits: It may not accurately convert recurring decimals, such as 0.333..., since it cannot represent infinite values. 
2. Edge Cases: Extremely small or large decimal values may lead to rounding errors during conversion. 
3. Assumptions: The tool assumes the input is a valid decimal; invalid inputs may produce errors or undefined results. 
4. Simplification: In certain cases, if the GCD is not calculated correctly due to manual errors, the fraction may not be fully simplified.

## FAQs

**Q:** How does the tool handle repeating decimals? 


**A:** The tool may not accurately convert repeating decimals, as it requires a finite representation to produce a fraction.


**Q:** Can this tool convert negative decimals to fractions? 


**A:** Yes, the tool can convert negative decimals, resulting in a fraction with a negative numerator.


**Q:** What if the decimal is a whole number? 


**A:** Whole numbers can be expressed as fractions by placing them over 1, e.g., 5 becomes 5/1.


**Q:** Is there a limit to the number of decimal places that can be converted? 


**A:** The tool can typically handle a standard number of decimal places, but precision may decrease with very large numbers.

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*Generated from [complete.tools/decimal-to-fraction](https://complete.tools/decimal-to-fraction)*