2.8 repeating as a fraction 

Cameron Mercado

Cameron Mercado

Answered question

2022-07-13

2.8 repeating as a fraction

 

Answer & Explanation

nick1337

nick1337

Expert2023-06-17Added 777 answers

To express the repeating decimal 2.8 as a fraction, we can use a technique called the method of differences. Let x = 2.8 (repeating).
First, we can multiply both sides of the equation by 10 to move the decimal point to the right: 10x = 28.8 (repeating).
Next, we subtract x from 10x to eliminate the repeating part: 10x - x = 28.8 - 2.8.
Simplifying this equation gives us: 9x = 26.
Finally, we divide both sides of the equation by 9 to solve for x: x = 26/9.
Therefore, the fraction representation of the repeating decimal 2.8 is 269.

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