Converting Fractions, Decimals and Percentages

In an interview you'll often be handed a fraction mid-calculation, "that's 7 out of 16 trades", and expected to say "about 44%" without reaching for a calculator or grinding out long division. The gap between candidates who freeze at that moment and candidates who answer instantly isn't raw calculation speed; it's that the fast ones have a small library of fraction-to-decimal conversions memorized cold, and know how to combine them for anything not directly in the library.

Build the library, don't derive it live

The core idea is to memorize a handful of "atomic" fractions and their decimal/percentage forms, then combine them by simple arithmetic instead of doing division from scratch every time. The atoms worth knowing:

• Halves and quarters: $1/2 = 0.5$, $1/4 = 0.25$, $3/4 = 0.75$.
• Thirds: $1/3 = 0.3\overline{3}$, $2/3 = 0.6\overline{6}$.
• Fifths: $1/5 = 0.2$, $2/5 = 0.4$, $3/5 = 0.6$, $4/5 = 0.8$.
• Eighths: $1/8 = 0.125$, $3/8 = 0.375$, $5/8 = 0.625$, $7/8 = 0.875$.
• Sixteenths: $1/16 = 0.0625$, each further sixteenth adds another $0.0625$.
• Sevenths: $1/7 \approx 0.142857$, repeating, worth knowing exists even if you don't memorize the digits.

In plain English: once you know $1/8 = 0.125$, you get $3/8$ for free by tripling it, and you get $7/16$ by noting it's close to $1/2 - 1/16 = 0.5 - 0.0625 = 0.4375$, you're composing known atoms, not dividing 7 by 16 longhand.

Worked example 1: 7/16 without long division

Recognize $16 = 4 \times 4$, so $1/16$ is a quarter of $1/4 = 0.25$, giving $1/16 = 0.0625$. Then $7/16 = 7 \times 0.0625$. Break the multiplication up: $7 \times 0.0625 = 7 \times 0.06 + 7 \times 0.0025 = 0.42 + 0.0175 = 0.4375$. So $7/16 = 43.75\%$, reached in three small steps, none harder than single-digit arithmetic.

Worked example 2: 11/12 as a deviation from 1

For fractions close to 1, it's faster to compute the gap than the fraction itself. $11/12 = 1 - 1/12$. You know $1/12 = \tfrac{1}{4} \times \tfrac{1}{3} = 0.25 \times 0.333... \approx 0.0833$. So $11/12 \approx 1 - 0.0833 = 0.9167$, i.e. about $91.7\%$. This "distance from a round number" trick is often faster than computing the fraction directly, especially for numerators close to their denominators.

What this means in practice

This skill isn't decorative, it's the substrate underneath every mental-math question that follows: computing a Sharpe ratio on the fly, sanity-checking a hedge ratio, converting a win rate into odds. If converting $5/8$ to a percentage takes you visible effort, every downstream calculation in the interview slows down and compounds into looking unprepared. Five minutes a day drilling the atoms above pays for itself almost immediately.