Multiplying Decimals

Multiply first, place the point last

Step 1: multiply as if there were no decimal points at all. $2.5 \cdot 1.3$ becomes $25 \cdot 13 = 325$.

Step 2: count the decimal places in both factors and add them up. $2.5$ has one place and $1.3$ has one place, so the product needs two: count two spots in from the right of $325$ to get $3.25$.

When you run out of digits, add zeros

Sometimes the whole-number product is too short for the places you need. $0.05 \cdot 0.3$: multiply $5 \cdot 3 = 15$, but the factors have three decimal places in total ($2 + 1$). Counting three spots into a two-digit number leaves a gap, so pad with a leading zero: $0.015$.

Write the zeros on the left of the digits, never the right — $0.015$, not $0.150$. Tacking a zero onto the right end changes nothing, but the gap you're filling is on the left.

Why counting places works

A decimal is a whole number that has been divided by $10$, $100$, or $1000$ — one division by $10$ per decimal place. $0.6$ is $6 \div 10$ and $0.3$ is $3 \div 10$. Multiply them and you get $18$ divided by $10$ twice, which is $18 \div 100 = 0.18$.

Every decimal place in a factor contributes one division by $10$ to the product. Counting places just tallies those divisions.

Worked examples

Try one yourself

Common questions