Final answer:
We can express the repeating decimal 0.326 bar 26 as the fraction p/q by using algebra to devise and solve an equation. The result is p/q equals 293/990.
Step-by-step explanation:
The number 0.326 with a bar over 26 represents a repeating decimal, meaning that the 26 repeats indefinitely. To express this as a fraction p/q, we represent it by using algebra. Let's denote the repeating decimal as x.
First, write down the decimal like so: x = 0.32626.... Then, multiply by a power of 10 that moves the decimal point to just after the non-repeating part: 100x = 32.62626.... The next step involves a further multiplication that makes the decimal parts of both expressions identical, allowing them to be subtracted out neatly: 10000x = 3262.62626....
Subtract the first equation from the second, which will eliminate the repeating part of the decimal: 9900x = 2930. Solving this equation gives x = 2930/9900. This fraction can be reduced by dividing both numerator and denominator by their greatest common divisor of 10, to give p/q = 293/990.
Learn more about Repeating Decimal to Fraction