Understanding 3/11 in Binary: A Deep Dive
Explore why the fraction 3/11 converts to a repeating sequence in binary and learn about its representation.
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3/11 in binary is a fraction represented as a repeating sequence, where the binary equivalent of the fraction converts to 0.0101100101... (repeating). Using IEEE 754 format, such representation becomes extensive in binary form and is generally rounded or symbolically expressed. Precise conversion involves detailed binary arithmetic.
FAQs & Answers
- What is 3/11 in binary? 3/11 is represented as a repeating binary sequence, specifically 0.0101100101... in binary form.
- How does IEEE 754 format work? IEEE 754 format is a standard for floating-point arithmetic that provides methods for representing and working with numbers in binary.
- Why are fractions repetitive in binary? Fractions can become repetitive in binary because not all decimal fractions can be expressed as finite binary representations.
- How to convert a fraction to binary? To convert a fraction to binary, you can use a method of multiplying by 2 and recording the integer part, but repeated calculations may lead to a repeating sequence.