Find the value of 2 . 357

Name: Problem 147, Chapter 9: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2021-08-25T16:21:53-08:00
Duration: 6 min 45 s
Channel: Sandip Ranjan
Description: Find the value of 2 . 357

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Key Concepts

Repeating Decimals

Repeating decimals are numbers where a digit or group of digits repeats infinitely beyond the decimal point. They are denoted with a bar over the repeating segment and exhibit a periodic pattern, which is a central concept in understanding the structure of rational numbers.

Conversion of Repeating Decimals to Fractions

This concept involves converting the infinite repeating part of a decimal into a finite fractional form. Typically, one sets up an equation representing the repeating decimal, multiplies by an appropriate power of 10 to align the repeating parts, and subtracts the original equation to eliminate the repetition. Solving this equation yields an exact fraction equivalent.

Mixed Numbers and Fraction Addition

When a repeating decimal includes a non-repeating whole number part, it forms a mixed number. The process involves converting the repeating decimal part into a fraction and then combining it with the whole number, ensuring the entire number is represented precisely in fractional form.

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