"0.1 + 0.1² + 0.1³ = ?" — GMAT® Worked Solution

From Episode 46 of Real GMAT® Problems (The GMAT® Strategy Podcast). For the full strategy behind computation on the GMAT®, read: GMAT® Computation: When to Do the Math (and When to Let Go).

The Problem

Source: Official Guide for GMAT® Review, 11th Edition

0.1 + 0.1² + 0.1³ = ?

(A) 0.1

(B) 0.111

(C) 0.1221

(D) 0.2341

(E) 0.3

Try it before reading on.

Why This Problem Matters

This is the kind of problem that can feel almost too easy. You see decimal exponents. You might know instinctively that the answer is 0.111. And you might be tempted to pick (B) without working through the steps.

That temptation is worth examining.

On the GMAT®, the scoring algorithm means that missing familiar problems has a larger negative effect on your score than missing hard ones. If you're 90% confident in your answer and skip the computation, you're accepting a 10% risk — and that risk costs more than the time you saved.

The habit worth building: on problems you know how to do, do the full math anyway. The goal is 100% confidence, not 90%.

Step 1: Compute 0.1²

0.1² = 0.1 × 0.1.

Set up the multiplication as if there were no decimal points.

1 × 1 = 1.

Now count the total decimal places in the numbers you multiplied.

0.1 has one decimal place. The other 0.1 has one decimal place. Total: two decimal places.

Shift the decimal point in the result two places to the left.

1.0 → 0.1 → 0.01.

0.1² = 0.01

Step 2: Compute 0.1³

0.1³ = 0.1² × 0.1 = 0.01 × 0.1.

Do 1 × 1 = 1.

Count decimal places: two from 0.01, one from 0.1. Total: three.

Shift three places left.

1.0 → 0.1 → 0.01 → 0.001.

0.1³ = 0.001

Step 3: Add the Three Terms

Line up the decimal places:

  0.100
  0.010
+ 0.001
-------
  0.111

Each column sums to 1. The result is 0.111.

The answer is (B).

What to Take Away

Count decimal places, then shift. When multiplying decimals, ignore the decimal points first. Do the whole-number multiplication. Then count the total decimal places across all the numbers you multiplied, and shift the decimal point that many places to the left. This works every time.

Line up the decimal points when adding. When adding decimals with different numbers of places, pad with zeros (0.100, 0.010, 0.001) so the columns align. Then add column by column just like whole numbers.

The algorithm rewards execution. Missing this problem costs more than missing a hard problem. The students who get this wrong aren't getting the math wrong — they're making careless errors while rushing. Slowing down on familiar problems is one of the highest-leverage habits you can build.

Ready for a harder one? The next problem adds a fraction structure and more decimal places, and the fraction conversion approach makes it much cleaner: (0.045 × 1.9) / (0.03 × 0.005 × 0.1) — Worked Solution.

Want the full strategy? Read: GMAT® Computation: When to Do the Math (and When to Let Go)

From Episode 46 of Real GMAT® Problems (The GMAT® Strategy Podcast).