Decimal Multiplication Calculator

Multiply decimals accurately with step-by-step examples, place value alignment, and consistent rounding. Enter two decimals, set precision, and get product with steps and tips.

Multiply Decimals

Result

4.08

Raw: 4.08

Work Steps

1
Remove decimal points
A = 12 (1 dp), B = 34 (1 dp)
2
Multiply as integers
12 × 34 = 408
3
Reinsert decimal point
Total decimal places = 1 + 1 = 2 → 4.08

What is Decimal Multiplication?

Place Value

Treat numbers as integers by removing decimal points, then reinsert the decimal using the total fractional digits across both factors.

Rounding

Use half-up for general math or banker’s rounding to reduce bias in aggregates. Set precision to control output decimal places.

How to Calculate Decimal Multiplication

Algorithm

1) Remove decimal points: record fractional digits of a and b

2) Multiply as integers

3) Reinsert decimal point using total fractional digits

4) Apply rounding mode and precision (optional)

Calculation Steps:

1
Remove decimals
Count fractional digits of a and b
2
Multiply integers
Use grade-school multiplication
3
Place decimal
Insert decimal using total fractional digits
4
Round (optional)
Half-up or banker’s; set precision

Important Considerations

⚠️ Rounding & Precision

For financial results, prefer banker’s rounding; for general math or education, half-up is fine.

Negative Numbers

Sign follows the rule: (+)×(+) or (-)×(-) → +, (+)×(-) → -

Trailing Zeros

Trim trailing zeros unless fixed precision is required for reporting.

Precision Bound

Practical precision range is 0–10 in this tool to keep output readable.

Very Small Numbers

If both inputs have many fractional digits, the product can be very small; increase precision if needed.

Example Cases

Case 1

Inputs: a = 1.2, b = 3.4, precision = 2, rounding = half-up

Product: 4.08
Raw: 4.08
Total dp: 2 (1+1)

Case 2

Inputs: a = -0.125, b = 0.2, precision = 3, rounding = banker’s

Product: -0.025
Raw: -0.025
Total dp: 4 (3+1)

Common Mistakes & Tips

Misplacing the Decimal

Count total decimal places across factors, then place the decimal point in the product accordingly.

Trailing Zeros

Trailing zeros after the decimal may be trimmed unless fixed precision is required.

Rounding Strategy

Use banker's rounding or standard half-up consistently; set precision before computing.

Place Value Alignment

Treat numbers as integers by removing decimals, multiply, then reinsert the decimal point.

Frequently Asked Questions

How do I multiply decimals?

Remove decimal points, multiply as integers, then place the decimal by counting total decimal places across factors. Optionally round to your desired precision.

How many decimal places will the product have?

Add the number of fractional digits from both factors. For example, 1.2 (1 dp) × 0.03 (2 dp) → product has 3 decimal places before rounding.

What rounding should I use?

Half-up is common for general use. Banker’s rounding reduces cumulative bias in financial or statistical contexts.

Why are there trailing zeros?

Zeros after the decimal that do not affect value can be trimmed. If fixed precision is required, keep them by setting precision.

Does order matter?

No. Decimal multiplication is commutative: a × b = b × a.