Quadratic Equation Solver (ax² + bx + c = 0)
About Reciprocal Calculator
The Multiplicative Inverse & Reciprocal ($1/x$) Calculator computes exact decimal, fractional ($a/b \rightarrow b/a$), and mixed number reciprocals with repeating decimal period analysis (e.g. $1/7 = 0.\overline{142857}$), scientific notation, and electrical impedance conversion.
How to Use Reciprocal Calculator
Step 1
Enter an integer, decimal, or fraction (e.g. `0.125` or `3/8`).
Step 2
Review computed reciprocal in fractional, decimal, and scientific notation.
Step 3
Inspect repeating decimal period length.
Step 4
Click "Copy Reciprocal".
Practical Use Cases for Reciprocal Calculator
Parallel Resistor & Capacitor Circuit Impedance Calculations
Compute equivalent resistance in parallel electronics circuits ($1/R_{eq} = 1/R_1 + 1/R_2 + 1/R_3$) with exact fractional precision.
Optics Focal Length & Diopter Lens Power Conversion
Convert focal lengths in meters to optical lens powers in diopters ($D = 1/f$) for optometry and camera lens design.
Input & Output Examples
Calculating Reciprocal of Fraction 7/12
Input: `7/12` (Decimal: `0.58333...`)
Reciprocal: `12/7` | Mixed Fraction: `1 5/7` | Decimal: `1.\overline{714285}` (Period: 6 digits)Key Features & Performance
- ✓Fraction Inversion: converts improper fractions, mixed numbers ($2\frac{3}{4} \rightarrow 4/11$), and decimals.
- ✓Repeating Decimal Analyzer: identifies non-terminating repeating periods and displays overline notation.
- ✓Handles arbitrary-precision floating point up to 50 decimal places.
- ✓100% Client-Side math engine.
- ✓1-Click Copy reciprocal fraction & decimal.
Key Terminology & Definitions
Multiplicative Inverse
A number which, when multiplied by $x$, yields the multiplicative identity 1 ($x \times (1/x) = 1$). Zero has no reciprocal.
Repeating Decimal Period
The sequence of repeating digits after the decimal point in a non-terminating rational fraction representation.