How to Multiply Decimals Step by Step (With Examples)

Multiplying decimals feels tricky because of the decimal point — but the point is the last thing you deal with. Multiply as if the numbers were whole, count decimal places to put the point back, then estimate to make sure the answer is the right size. That's the whole method.

The 3-step method

1. Multiply as whole numbers. Ignore the decimal points completely.
2. Count decimal places. Add up the digits after the point in both numbers.
3. Place the point and estimate. Put that many digits after the point in your answer, then compare with a rounded estimate.

Worked example: $0.58 \times 3.25$

Step 1 — Multiply as whole numbers

Remove the points: $58 \times 325$. Using long multiplication:

• $325 \times 8 = 2600$
• $325 \times 50 = 16250$
• Add the partial products: $2600 + 16250 = 18850$

Step 2 — Count decimal places

$0.58$ has 2 decimal places and $3.25$ has 2, so the answer needs $2 + 2 = 4$ decimal places: $18850 \rightarrow 1.8850$.

Trailing zeros after the decimal point don't change the value, so $0.58 \times 3.25 = 1.885$.

Step 3 — Estimate to check

Round each factor: $0.58 \approx 0.6$ and $3.25 \approx 3$. $0.6 \times 3 = 1.8$. Our answer, $1.885$, is close to $1.8$ — so the decimal point is in the right place. If we had written $18.85$ or $0.1885$, the estimate would catch it instantly.

More examples

$2.27 \times 2.2$

Whole numbers: $227 \times 22 = 4994$. Decimal places: $2 + 1 = 3$. Answer: $4.994$. Estimate: $2 \times 2 = 4$ ✓.

Tiny numbers: $0.0945 \times 1.47$

Whole numbers: $945 \times 147 = 138915$. Decimal places: $4 + 2 = 6$. Answer: $0.138915$. Estimate: $0.1 \times 1.5 = 0.15$ ✓.

Notice the zeros right after the decimal point in $0.0945$ still count as decimal places.

Three decimals: $3.1 \times 4.4 \times 6.3$

Multiply two at a time. $3.1 \times 4.4$: $31 \times 44 = 1364$, two places → $13.64$. Then $13.64 \times 6.3$: $1364 \times 63 = 85932$, three places → $85.932$. Estimate: $3 \times 4 \times 6 = 72$, so 85.9 is a sensible size ✓.

When the zeros cancel: $6.4 \times 2.5$

$64 \times 25 = 1600$, two places → $16.00 = 16$.

Multiplying by 10, 100 and 0.1

• × 10 moves the point one place right: $3.25 \times 10 = 32.5$
• × 100 moves it two places right: $3.25 \times 100 = 325$
• × 0.1 moves it one place left: $3.25 \times 0.1 = 0.325$

Common mistakes

• Lining up decimal points as you would for addition — not needed for multiplication.
• Counting decimal places in only one number.
• Dropping the leading zeros that hold place value (writing $0.13891$ instead of $0.138915$ because a digit was lost).
• Skipping the estimate, which is the easiest way to catch a misplaced point.

Use a step-by-step multiplication calculator

To see the full long multiplication for your own numbers, use the step-by-step multiplication calculator. For very small or very large products, the scientific notation calculator keeps the digits manageable. Division is the reverse operation — see dividing with remainders.

FAQ

How do you multiply decimals step by step? Multiply the numbers as whole numbers, count the total decimal places in both factors, and place the decimal point that many digits from the right.

Do I need to line up the decimal points? No. That's for adding and subtracting. For multiplication, only the total count of decimal places matters.

What is 0.58 × 3.25? $1.885$ (from $58 \times 325 = 18850$ with four decimal places).

Can the answer be smaller than both numbers? Yes, when you multiply by a number less than 1. For example, $0.5 \times 0.4 = 0.2$.

How do I check my answer quickly? Round each number to one significant figure and multiply. Your exact answer should be close to the estimate.

Is there a multiplication calculator with steps? Yes — the step-by-step multiplication calculator shows each partial product.

Further reading: OpenStax Prealgebra 2e, chapter 5 "Decimals".