"(0.045 × 1.9) / (0.03 × 0.005 × 0.1) = ?" — 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

0.045 × 1.90.03 × 0.005 × 0.1 = ?

(A) 5,700

(B) 570

(C) 57

(D) 5.7

(E) 0.57

Try it before reading on.

Why This Problem Trips People Up

The answer choices are all the same digits — just with the decimal point in different positions. The math is entirely about tracking decimal places correctly.

That's the trap. If you try to do this in decimal form, you have five numbers with decimal places to track simultaneously. The risk of dropping or miscounting one is high.

The cleaner path: convert every decimal to a fraction before touching the math. Then the computation becomes integer multiplication and cancellation.

Step 1: Convert Every Decimal to a Fraction

Each decimal becomes a fraction over the appropriate power of 10.

0.045 → 451,000 (three decimal places = over 1,000)

1.9 → 1910 (one decimal place = over 10)

0.03 → 3100

0.005 → 51,000

0.1 → 110

Step 2: Rewrite the Expression

The numerator becomes:

451,000 × 1910

The denominator becomes:

3100 × 51,000 × 110

Step 3: Flip and Multiply

Dividing by a fraction is the same as multiplying by its reciprocal. Flip every fraction in the denominator and multiply everything across.

451,000 × 1910 × 1003 × 1,0005 × 101

Step 4: Cancel Zeros

Look for zeros in the numerators and denominators and cancel them.

1,000 on top cancels with 1,000 on the bottom.

100 on top cancels with 1,000 on the bottom (partially — leaves 10 on top).

Wait — let's be precise. Collect all numerators and denominators:

Numerators: 45 × 19 × 100 × 1,000 × 10

Denominators: 1,000 × 10 × 3 × 5 × 1

Cancel 1,000 from both sides. Cancel 10 from both sides. You're left with:

45 × 19 × 1003 × 5

Step 5: Cancel Numerically

3 × 5 = 15. And 45 = 15 × 3. So we can cancel 45 with 15, leaving 3.

3 × 19 × 1001

3 × 19 = 57. 57 × 100 = 5,700.

The answer is (A).

What to Take Away

One approach works for most decimal computation problems. Convert to fractions. Flip the denominator fractions. Multiply across. Cancel zeros. The computation almost always collapses into manageable integer math.

You don't need a different trick for every problem type. A lot of test prep advice tells you to memorize specific decimal shortcuts for specific situations. That works for some people. But if it's not working for you — if you end up with a different trick for every problem — the fraction conversion approach is a more reliable fallback.

If you're close to test day, go all-in on fractions. Decimal computation requires practice and solid number sense. If you haven't built that yet and the test is soon, switching everything to fraction form is a defensible strategy. It works on almost every problem in this category.

Ready for the hard one? The third problem combines fractions, exponents, and decimal long division — and adds a decision about when to brute-force and when to let go: x = 1/(2² × 3² × 4² × 5²), Distinct Non-Zero Digits — 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).