Enter Fraction Values
Formula Used
For 5/4, the exact result is √5/2. Its decimal value is about 1.1180339887. This value is irrational and never terminates exactly.
How to Use the Calculator
- Enter the fraction numerator.
- Enter a nonzero denominator.
- Select decimal precision and denominator limit.
- Choose the preferred result display mode.
- Press Calculate to generate exact and approximate results.
- Copy, print, or export the completed calculation.
Example Calculations
| Expression | Exact result | Decimal result | Classification |
|---|---|---|---|
| √(5/4) | √5/2 | 1.118034 | Irrational |
| √(9/16) | 3/4 | 0.75 | Rational |
| √(8/9) | 2√2/3 | 0.942809 | Irrational |
| √(12/25) | 2√3/5 | 0.692820 | Irrational |
| √(2/3) | √6/3 | 0.816497 | Irrational |
Exact and Approximate Results
An exact radical preserves the complete mathematical value. A decimal only shows a rounded approximation. Fraction approximations depend on the chosen denominator limit.
For √5/2, no integer fraction is exact. Increasing the denominator limit usually improves accuracy. The displayed error measures the remaining decimal difference.
Common Mistakes
- Using zero as the denominator.
- Assuming every square root is rational.
- Rounding before radical simplification finishes.
- Forgetting that negative inputs produce imaginary values.
- Treating a close fraction approximation as exact.
Frequently Asked Questions
What is the exact square root of 5/4?
The exact answer is √5/2. The denominator square root simplifies to two. The numerator remains an irrational radical value.
Can √5/2 be written as an exact integer fraction?
No integer fraction equals √5/2 exactly. The value is irrational and nonterminating. Fractions can only provide close approximations.
Why does the calculator rationalise radicals?
Rationalisation removes radicals from denominators. It creates a conventional simplified form. The mathematical value remains completely unchanged.
What does maximum denominator mean?
It limits the approximation fraction denominator. Larger limits may produce closer fractions. Smaller limits create simpler readable approximations.
Does the calculator accept decimal inputs?
Yes, it converts decimals into fractions first. Up to eight decimal places are accepted. Exact simplification then uses integer arithmetic.
What happens with a negative fraction?
A negative radicand produces an imaginary result. The calculator displays an i factor. Percentage output becomes unavailable for that result.
How is the approximation error calculated?
The calculator subtracts the fraction approximation from the decimal magnitude. It then uses the absolute difference. Smaller errors indicate closer approximations.
What is a continued fraction?
It represents a number using nested reciprocals. Continued fractions reveal strong rational approximations. Irrational values produce continuing term sequences.
Can I export the calculation?
Yes, results can be copied directly. CSV and PDF downloads are included. Printing is also available from the browser.