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What is the rational number equivalent to 1 point 28 with a bar over 28? 1 and 6 over 97 1 and 28 over 99 1 and 8 over 33 1 and 5 over 16

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Yna9141
In algebra, the conversion of a more complex number to a simpler mixed number is rather simple. For the repeated numbers, which are designated by the bar above them, we simply have to put over 9 for each number repeated and 0 for the non-repeated numbers.

In this item, we have 1.28 with bar above 28 signifying that the number can also be written as 1.28282828.... The mixed number is then equal to,
1 and 28/99 or 1 and 28 over 99

Therefore, the answer to this item is the second choice. 

Answer: The answer is [tex]1\dfrac{28}{99}.[/tex] .

Step-by-step explanation: The given rational number is

[tex]R=1.\bar{28}.[/tex]

We are to select the correct expression from the options  that is equivalent to the given rational number.

Let us consider that

[tex]x=1.\bar{28}\\\\\Rightarrow x=1.28\bar{28}\\\\\Rightarrow 100\times x=100\times 1.28\bar{28}\\\\\Rightarrow 100x=128.\bar{28}\\\\\Rightarrow 100x=128+.\bar{28}\\\\\Rightarrow 100x=127+x\\\\\Rightarrow 100x-x=127\\\\\Rightarrow 99x=127\\\\\Rightarrow x=\dfrac{127}{99}\\\\\Rightarrow x=1\dfrac{28}{99}.[/tex]

Thus, the correct option is [tex]1\dfrac{28}{99}.[/tex]