How do you convert 2.8 (8 being repeated)

Answered question

2022-08-27

How do you convert 2.8 (8 being repeated) to a fraction?


 

Answer & Explanation

Vasquez

Vasquez

Expert2023-05-29Added 669 answers

To convert the decimal number 2.8 (with the 8 repeating) to a fraction, we can use algebraic techniques. Let's call the decimal number x:
x=2.8 (8 being repeated)
To remove the repeating part, we can multiply both sides of the equation by a power of 10 that will shift the repeating part to the left of the decimal point. In this case, we can multiply by 10^1 (which is 10):
10x=28.8 (8 being repeated)
Now, let's subtract the original equation (x) from the new equation (10x) to eliminate the repeating part:
10xx=28.8 (8 being repeated) - 2.8 (8 being repeated)
Simplifying the equation:
9x=26
To isolate x, we divide both sides of the equation by 9:
9x9=269
Simplifying further:
x=269
Therefore, the decimal number 2.8 (8 being repeated) is equal to the fraction 269.

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