Question

Which of the following rational numbers is equal to 2 point 8 with bar over 8 ? twenty two over nine, twenty four over nine, twenty six over nine, twenty eight over nine

Answer 1

Answer:

its 26/9 just divided all the numbers by 9

ex. 22 divided by 9 is 2.4

Step-by-step explanation:

Answer 2

Just to remove ambiguities, the bar over the expression means it's repeating itself to infinity.

$\bf 2.888\overline{8}\impliedby \textit{now say, let's make }x=2.888\overline{8} \\\\\\ \textit{and multiply it by 10, to move over the 8 to the left} \\\\\\ \begin{array}{llll} 10x&=&10\cdot 2.888\overline{8}\\ &&28.88\overline{8}\\ &&26+2.888\overline{8}\\ &&26+x \end{array}\implies 10x=26+x \\\\\\ 9x=26\implies x=\cfrac{26}{9}$

notice, the idea being, you multiply it by 10 at some power, so that you move the "recurring decimal" to the other side of the point, and then split it with a digit and "x".

now, you can plug that in your calculator, to check what you get.