Technique Encyclopedia

Estimation

What it is

Estimation means rounding the numbers in a computation to something easy to work with mentally, then computing with those rounded values instead of the exact ones. On a multiple-choice test, this is often all that's needed — if the answer choices are spread far apart, a rough approximation lands closer to one option than any other.

Signals that suggest using it

The exact computation involves messy decimals, large numbers, or awkward fractions.
Answer choices are spread far apart, so precision beyond a rough estimate isn't needed.
The problem includes words like "approximately" or "closest to."

When it's effective

Ideal when answer choices are well-separated — rounding aggressively is safe, since even a generous approximation error won't cross into a neighboring choice.

When it's not effective

If the answer choices are close together, a rough estimate risks landing near the boundary between two options — exact computation, or at least tighter bounding, becomes necessary instead.

Simple example

Problem

Estimate the value of 4.98 × 20.1.

Solution

Round each factor to the nearest convenient number: 4.98 rounds to 5, and 20.1 rounds to 20. 5 × 20 = 100. (The exact value is about 100.1 — the estimate is essentially exact here.)

AMC-style example

Problem

Which is closest to 203 × 0.049 × 5.1?

Solution

Round each factor: 203 → 200, 0.049 → 0.05, 5.1 → 5. Then 200 × 0.05 × 5 = 50. (The exact value is about 50.7 — close enough that 50 is clearly the best estimate among typical answer choices.)

Bounding Exploiting Answer Choices