is 1/26 a recurring number??

Yep......any integer ratio [ assuming the numerator/ denominator isn't 0 ] can always be expressed as either a terminating decimal, or one that has a repeating pattern

If the denominator can be factored in terms of 2 and/or 5  only, the decimal expression of the fraction terminates.....otherwise, the decimal representation of the fraction has a repeating pattern

Since 26 factors as 13 * 2.......the denominator isn't expressed in terms of 2 and/or 5 only, so we have a repeating pattern