Converting Fractions to Decimals at Interview Speed

Sevenths, elevenths, thirteenths and ninths each repeat in a fixed digit block, and memorizing those blocks replaces long division under a clock.

Converting a fraction to a decimal at interview speed means recognizing a small set of repeating patterns rather than performing long division from scratch every time. Sevenths, elevenths, ninths and thirteenths each produce a repeating block of digits that stays the same no matter which fraction from that family you are asked to convert, and memorizing the block for each denominator turns six or seven distinct conversions into one pattern per denominator.

One seventh is 0.142857 repeating, and every other seventh is the same six digits rotated to a different starting point. Two sevenths is 0.285714, three sevenths is 0.428571, four sevenths is 0.571428, five sevenths is 0.714285, and six sevenths is 0.857142. Once the digit string 142857 is memorized, converting any seventh is a matter of finding where in that cycle the block should start.

The starting point follows a simple rule: track which multiple of one seventh you are converting and read off the block from the position that numerator occupies in the rotation 1, 4, 2, 8, 5, 7 for one seventh and its multiples. In practice, most candidates find it faster to just memorize all six rotations directly rather than deriving the starting point each time.

Elevenths repeat in a two-digit block rather than a six-digit one. One eleventh is 0.090909 repeating, two elevenths is 0.181818, and three elevenths is 0.272727, each one simply the numerator times 9 written as a two-digit block and repeated. Nine times 3 is 27, which is exactly the repeating block for three elevenths.

This shortcut works cleanly up to ten elevenths, since 9 times 10 is 90, still a two-digit number, and breaks down past that point since the block would need three digits. For interview purposes, the fractions that actually appear rarely go past five or six elevenths, so the two-digit multiplication rule covers essentially every case that comes up.