Multiplying Decimals

To multiply decimals, multiply as if the points were not there, then put the point back. Take 0.3 × 0.7. As whole numbers, 3 · 7 is 21. Each factor has one decimal place, so the answer has 1 + 1 = 2 places: 0.21.

Why count places? 0.3 is 3 tenths and 0.7 is 7 tenths, and a tenth of a tenth is a hundredth. Money shows it: a tenth of a dollar is 10 cents, and a tenth of that is 1 cent, a hundredth of a dollar. So 3 tenths times 7 tenths is 21 hundredths, which is 0.21.

Sometimes the whole-number product is too short for the places it needs. In 0.2 × 0.3, 2 · 3 is 6, but the answer needs two places, so a zero fills in: 0.06. Notice the product is smaller than both factors. Multiplying by a number less than 1 takes only a part of something, so the result shrinks.