Is the product always bigger?

With fractions you saw that the product is not always greater than the numbers multiplied. Decimals are just another way of writing fractions, so the same thing happens — and it is worth checking with decimal examples.

Take 2.25 × 8 = 18. The product, 18, is greater than 2.25 and greater than 8. That is the familiar case.

Now 0.25 × 8 = 2. The product is greater than 0.25, but LESS than 8. It has landed between the two numbers.

And 0.25 × 0.8 = 0.2. Now the product is less than 0.25 AND less than 0.8 — smaller than both.

So when is the product greater than both, and when less? It depends, exactly as with fractions, on whether each number is between 0 and 1 or greater than 1.

Situation 1: both numbers greater than 1, as in 3.4 × 6.5 = 22.1. The product is greater than both. Situation 2: both between 0 and 1, as in 0.75 × 0.4 = 0.3. The product is less than both.

Situation 3: one between 0 and 1 and one greater than 1, as in 0.75 × 5 = 3.75. The product is less than the number greater than 1, and greater than the number between 0 and 1 — it lands between them. The short version is the same as before: multiplying by something less than 1 shrinks, and multiplying by something more than 1 grows.