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.