# Why Does Math.round(0.49999999999999994) Round to 1?

DevFeed: [Why Does Math.round(0.49999999999999994) Round to 1?](<https://devfeed.tech/articles/why-does-math-round-0-49999999999999994-round-to-1-30750.md>)

Original publisher: [Read original article](<http://blog.vanillajava.blog/2024/12/why-does-mathround049999999999999994.html>)

Author: Peter Lawrey (noreply@blogger.com)

Published: 2024-12-07T21:02:00Z

Content type: tutorial

Language: en

Sources: [Vanilla Java](<https://devfeed.tech/sources/vanilla-java.md>)

Topics: [floating-point](<https://devfeed.tech/topics/floating-point.md>), [Java](<https://devfeed.tech/topics/java.md>), [Programming](<https://devfeed.tech/topics/programming.md>), [implementation](<https://devfeed.tech/topics/implementation.md>)

Tags: [article](<https://devfeed.tech/tags/article.md>), [code](<https://devfeed.tech/tags/code.md>), [exercise](<https://devfeed.tech/tags/exercise.md>), [floating-point](<https://devfeed.tech/tags/floating-point.md>), [info](<https://devfeed.tech/tags/info.md>), [java](<https://devfeed.tech/tags/java.md>), [precision](<https://devfeed.tech/tags/precision.md>), [programming](<https://devfeed.tech/tags/programming.md>), [puzzles](<https://devfeed.tech/tags/puzzles.md>)

## AI overview

This article explains why Java 6 can return 1 when Math.round() is applied to a value slightly below 0.5. It attributes the result to binary floating-point representation, rounding behavior, and implementation details, and contrasts Java 6 with Java 7.

## Source excerpt

1. Defining the Problem In many numerical computations, one would reasonably expect that rounding 0.499999999999999917 should yield 0, since it appears to be slightly less than 0.5. Yet, in Java 6, calling Math.round() on this value returns 1, a result that may initially seem baffling. This seemingly minor discrepancy stems from the interplay of binary floating-point representation, rounding modes, and the particular internal implementation details of Math.round() in earlier Java releases. For professionals in performance-sensitive environments--such as those working in financial technology or high-precision scientific applications--understanding these subtleties is more than just an academic exercise. Even tiny rounding differences can influence trading algorithms, pricing models, or simulations. Moreover, developers and enthusiasts who appreciate the low-level mechanics behind Java's numeric types will find valuable insights into how these internal workings affect everyday programming tasks. This article delves into why this unexpected rounding occurs, sheds light on the constraints of double-precision arithmetic, and contrasts the behaviour in Java 6 against newer versions like Java 7. Consider, for instance, the closely related question: Why does Math.round(0.49999999999999994) return 1 rather than 0? Although it might initially seem like a bug, it is, in fact, a predictable outcome once we acknowledge the inherent imprecision of floating-point arithmetic. By the end, you will have a clearer understanding of why these rounding anomalies happen, and how to avoid or mitigate their effects in your own code. 2. The IEEE 754 64-bit Double-Precision Format Component Bit Count Interpretation Sign 1 Determines the sign of the number: 0 indicates a positive value, 1 indicates a negative value. Exponent 11 Encodes the exponent using a bias of 1023. The stored value E is interpreted as E - 1023 for the actual exponent. Mantissa (Fraction) 52 Represents the significand (fract