Wiki Article · Cinematic

Rounding Error

Rounding error (ya round-off error) ek aisi numerical inaccuracy hai jo tab hoti hai jab kisi real…

Overview

Rounding Error — Quick Facts

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Property: Detail

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Also Known As: Round-off error, Floating-point…

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Category: Numerical Computing, Computer…

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Domain: Mathematics, Software Engineering,…

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Infobox

📚 | Property | Detail | |---|---| | Also Known As | Round-off error, Floating-point error,…

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Mermaid Diagram: Rounding Error Lifecycle

💡 `mermaid flowchart TD A["Real Number (e.g. 0.1)"] --> B["Binary Conversion"] B -->…

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1. Taaruf aur Bunyaadi Samajh

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Single calculation me error…

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Repeated calculations me error…

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Comparison operations (==)…

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Financial transactions me…

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2. IEEE 754 Standard — Floating-Point ka Foundation

⭐ IEEE 754 duniya ka sabse widely used standard hai floating-point arithmetic ke liye. 1985…

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3. Rounding Error ke Types

🔑 Rounding error ek broad term hai — iske andar multiple subtypes hain, har ek ka specific…

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4. Error Propagation aur Accumulation

✨ Ek single rounding error chhota hota hai, lekin jab calculations chain me hoti hain, to…

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5. Catastrophic Cancellation

🌟 Catastrophic cancellation tab hoti hai jab do nearly equal numbers ka difference lete…

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6. Machine Epsilon aur ULP

🚀 Machine Epsilon ($\epsilon_{mach}$) Machine epsilon smallest positive number hai jiska $1…

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7. Real-World Disasters

📚 Rounding error sirf theoretical problem nahi — isne real-world me deaths, financial…

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8. Programming Languages me Rounding Behavior

💡 Har language IEEE 754 follow karti hai, lekin default types, precision, aur utility…

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9. Numerical Stability Techniques

🎯 9.1 Kahan Summation Algorithm Standard summation me rounding error accumulate hota hai.…

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10. Financial aur Scientific Computing

⭐ Financial Computing Financial systems me rounding error kabhi acceptable nahi —…

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11. Testing aur Detection Strategies

🔑 Floating-Point Testing Rules | Rule | Description | |---|---| | Never use == for float…

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12. Mitigation Best Practices

✨ 1. Decimal types use karo financial aur monetary calculations me — kabhi float mat use…

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13. Rounding Methods Comparison

🌟 | Method | IEEE 754 Name | Bias | Default In | Best For | |---|---|---|---|---| | Round…

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Glossary

🚀 | # | Term | Definition | |---|---|---| | 1 | Rounding Error | Finite precision…

Comparison

13. Rounding Methods Comparison

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Round Half Even: roundTiesToEven

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Round Half Up: —

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Round Half Down: —

Diagram

Visual Flow

📊 Diagram visualization — details in narration

Quick Quiz

Quiz — Question 1

Rounding Error ka sabse sahi definition kya hai?

Quick Quiz

Quiz — Question 2

Rounding Error ka 'Also Known As' kya hai?

Complete! 🎉

Rounding Error Complete!

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