You have finished a calculation and landed at \dfrac{49}{36}. The options on the paper say 1.361, 1.36, \tfrac{49}{36}, 1.4. Your finger hovers over the calculator. Should you punch the fraction in and pick the decimal that matches, or should you leave the answer as it is?

The short answer: keep the fraction until the last step, and only convert to a decimal if the question or the options force you to. In JEE-style problems this is not a stylistic preference — it is the difference between the right answer and the wrong answer in a one-mark question decided by rounding in the third decimal.

Fractions are exact, decimals round

A fraction \dfrac{p}{q} in lowest terms is a precise number. \dfrac{1}{3} is \dfrac{1}{3}, not 0.33, not 0.333, not 0.33333. A decimal is only ever a snapshot — you stop writing digits after some number of places, and whatever comes after that point is chopped off.

The rounding is silent and cumulative. Start with \tfrac{1}{3} \approx 0.333 — you have already thrown away everything from the fourth decimal onward, so you are carrying an error of about 3 \times 10^{-4}. Multiply that by something large, or subtract two nearly-equal decimals, and the error can blow up into the first or second decimal place — right where the MCQ options differ.

Error accumulation when truncating one third to a decimalTwo horizontal bars stacked. The top bar labelled exact fraction shows one third carried symbolically through five operations, with a green tick indicating zero error at the end. The bottom bar labelled truncated decimal shows zero point three three three three carried through the same operations, with the error growing from tiny at the start to visible at the end, marked with a red cross at the final step where the fourth decimal has drifted. fraction route: 1/3 → × 6 = 2 → + 1/3 = 7/3 → × 3 = 7 every step is exact; final answer is the integer 7 decimal route: 0.3333 → × 6 = 1.9998 → + 0.3333 = 2.3331 → × 3 = 6.9993 answer is 6.9993, off from the true 7 by 0.0007 if the option is "7" and "6.99," rounding loses a mark
The same calculation along two routes. The fraction route keeps $\tfrac{1}{3}$ symbolic, and every step lands on a clean integer. The decimal route truncates to four places at the start and the error compounds — by the end, the answer is $6.9993$ instead of the true $7$. In a four-option MCQ where the choices are $7$, $6.99$, $\tfrac{7}{1}$, $7.1$, the decimal route is one rounding away from the wrong letter.

Why: every time you truncate, you introduce an error of up to half a unit in the last decimal kept. Arithmetic operations propagate that error — multiplication by a large number amplifies it, and subtraction of nearly-equal decimals (so-called "catastrophic cancellation") can make the error dominate the answer entirely.

The rule of thumb

When you do a JEE problem, think of the calculation as a pipeline:

  1. Set up — write everything as fractions or as symbolic expressions (\sqrt{2}, \pi, \sin 30°). No decimals yet.
  2. Simplify — cancel common factors, combine fractions, use identities. Still no decimals.
  3. Final answer — if the options are fractions or surds, stop here. If the options are decimals, then — and only then — convert.

The rule is: defer decimal conversion as long as possible. Fractions compose cleanly; decimals drift.

What the question signals

JEE questions are careful about the form they expect. Read the stem and the options:

Flowchart for deciding whether to convert an answer to a decimalA simple flowchart. The top box asks does the question or the answer options demand a decimal. The yes branch goes to a box labelled convert at the final step only using enough decimal places. The no branch goes to a box labelled leave as a fraction or surd. Both paths end at a common bottom box labelled now submit the answer. do the options ask for a decimal? (or does the stem say "correct to n decimals"?) no yes keep it as a fraction or surd, or π — don't touch decimals convert at the final step use one more decimal than options differ by submit the answer
The decision reduces to a single question: does the form of the answer demand a decimal? If not, leave it as a fraction or surd. If yes, convert at the final step with enough precision that the answer matches exactly one option.

Three situations where decimals cost marks

Probability. A probability problem lands at \tfrac{7}{36}. The options are \tfrac{7}{36}, \tfrac{5}{24}, \tfrac{1}{6}, \tfrac{1}{4}. If you convert to 0.194 and eyeball, you might pick \tfrac{5}{24} \approx 0.208 or \tfrac{1}{6} \approx 0.167 because they look "close." But the fraction \tfrac{7}{36} is sitting right there as an option. Cross-check fractions with fractions, never with decimals.

Integration answers. An integral evaluates to \dfrac{\pi}{4} - \dfrac{1}{2}. The options contain \dfrac{\pi - 2}{4}. If you decimalise you see 0.785 - 0.5 = 0.285 and the option gives (3.14 - 2)/4 = 0.285. They agree — but this is slower and noisier than recognising that \tfrac{\pi}{4} - \tfrac{1}{2} = \tfrac{\pi - 2}{4} directly by common denominator. Fraction arithmetic was faster and exact.

Trigonometric identities. A trigonometry problem simplifies to \sin 75° = \tfrac{\sqrt{6} + \sqrt{2}}{4}. Decimalising gives 0.9659. An option reads \tfrac{\sqrt{3} + 1}{2\sqrt{2}}. Is that the same number? Decimalise and you get 0.9659 — match — but you have not proved the match. If the true answer is slightly different by a \sqrt{2} factor somewhere, the decimal approximation might fool you. Staying in surds lets you rationalise and compare algebraically, with no room for ambiguity.

When decimals are the right answer

There are three common situations where converting early is fine or even preferred.

The distinction is between using a decimal as a scratchpad tool (fine, keep doing it) and using a decimal as the final carried answer (not fine, unless asked for).

A tiny example

Compute \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{6}.

Fraction route. Common denominator 6. \tfrac{3}{6} + \tfrac{2}{6} + \tfrac{1}{6} = \tfrac{6}{6} = 1. The answer is exactly 1, and you arrive at it without any decimals.

Decimal route. 0.5 + 0.333 + 0.167 = 1.000. The answer looks like 1, but the "0.333" and "0.167" are rounded, and you are really computing 0.5 + 0.3333\dots + 0.1666\dots = 0.9999\dots, which requires a separate argument (see why 0.999\dots = 1) to conclude equals exactly 1. The fraction route lands on 1 with no such detour.

Two routes to computing one half plus one third plus one sixthTwo parallel paths to the same answer. The fraction path shows one half plus one third plus one sixth with a common denominator of six, giving three sixths plus two sixths plus one sixth equals six sixths equals one. The decimal path shows zero point five plus zero point three three three plus zero point one six seven equals nine point nine nine nine tenths, with a question mark indicating the answer is only approximately one. fractions 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1 exactly decimals (3-place) 0.5 + 0.333 + 0.167 = 1.000 but only because of rounding — truly 0.9999… ≈ 1
Two routes, same answer. Only the fraction route gets to the exact answer without a rounding argument. The decimal route happens to land on $1.000$ but only because the rounding of $\tfrac{1}{3}$ and $\tfrac{1}{6}$ happened to cancel — a coincidence, not a guarantee.

What to remember

JEE scoring is rigid — an option matched by rounding is still the wrong option if the exact computation would have picked a different one. The habit of staying in fractions until the last possible moment is not pedantry; it is how to keep marks.

Related: Fractions and Decimals · What's the Quickest Way to Compare 7/9 and 11/15 in My Head? · How to Know If a Fraction Terminates or Repeats — Without Doing the Division · Why Is 0.333… Exactly 1/3 and Not Just Very Close to It?