Decimal Fraction Formula Calculator
Convert any decimal number into a simplified fraction and mixed number. View step-by-step denominator expansion ($10^n$), greatest common divisor (GCD) simplification, and repeating decimal handling.
Formula & Mathematical Methodology
Count the number of decimal digits n, place the decimal over 10ⁿ to create a raw fraction, and divide both numerator and denominator by their greatest common divisor (GCD).
How to Use This Decimal Fraction Formula Calculator
- Enter the decimal number in the input box.
- Specify if the decimal has an infinitely repeating digit cycle.
- View the simplified fraction, mixed number, unreduced fraction, and GCD reduction steps.
Step-by-Step Worked Example
Scenario: Convert 0.375 into a simplified fraction
What Does Your Result Mean?
Fractions represent precise rational numbers without any decimal truncation or rounding inaccuracies.
Common Practical Applications:
- Converting digital caliper readings to wrench and socket sizes
- Simplifying decimal results in algebra and physics homework
- Cooking and tailoring adjustments requiring exact fractional parts
Important Limitations & Assumptions:
- Irrational numbers (such as π or √2) cannot be represented as exact fractions of integers.
Frequently Asked Questions
How do you convert a decimal into a fraction?
Write down the decimal divided by 1 (e.g. 0.75/1). Multiply top and bottom by 10 for every number after the decimal point (75/100), then simplify using their greatest common factor (3/4).
How do you convert a repeating decimal to a fraction?
Set x equal to the decimal (e.g. x = 0.333...). Multiply by 10 (10x = 3.333...). Subtract the first equation from the second: 9x = 3, so x = 3/9 = 1/3.
What is 0.375 as a fraction in simplest form?
0.375 = 375/1000. Dividing both top and bottom by their GCD of 125 gives 3/8.