To divide any number by zero will give infinity and therefore an error.
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Repeating decimal
Yes, 0.777777777777 is a rational number. A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. In this case, 0.777777777777 can be expressed as 7/9, which is a ratio of two integers. Therefore, it is a rational number.
By demonstrating that it is equivalent to the ratio: 57/100. Any number that can be expressed as the ratio of two integers, the denominator not equal to zero, is rational.
It cannot be zero.
Rational expressions are fractions and are therefore undefined if the denominator is zero; the domain of a rational function is all real numbers except those that make the denominator of the related rational expression equal to 0. If a denominator contains variables, set it equal to zero and solve.