Multiplying Decimals Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Multiplying Decimals.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Multiplying numbers that contain decimal points by first multiplying as if they were whole numbers, then placing the decimal point in the product based on the total number of decimal places in both factors.

Think of 0.3×0.40.3 \times 0.4 as 310×410=12100=0.12\frac{3}{10} \times \frac{4}{10} = \frac{12}{100} = 0.12. When you multiply decimals, you're working with fractions of 10, so the answer gets smaller—not bigger.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Multiplying decimals multiplies the numbers as whole numbers, then puts the decimal point so the product has as many decimal places as both factors combined.

Common stuck point: The procedure for multiplying decimals is the easy part; the trap is aligning decimal points like addition. Asking "Am I multiplying decimals by computing the whole-number product then counting decimal places?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I multiplying decimals by computing the whole-number product then counting decimal places?

Worked Examples

Example 1

easy
Calculate 0.4×30.4 \times 3.

Answer

1.2

First step

1
Think of 0.40.4 as 4×0.14 \times 0.1.

Full solution

  1. 2
    0.4×3=(4×0.1)×3=4×3×0.1=12×0.1=1.20.4 \times 3 = (4 \times 0.1) \times 3 = 4 \times 3 \times 0.1 = 12 \times 0.1 = 1.2.
  2. 3
    Or: multiply 4×3=124 \times 3 = 12, then place decimal: 1 decimal place → 1.21.2.
To multiply a decimal by a whole number, multiply as integers then place the decimal point. 4×3=124 \times 3 = 12, one decimal place → 1.2.

Example 2

medium
Calculate 2.3×1.42.3 \times 1.4.

Example 3

easy
Multiply: 0.3×0.70.3 \times 0.7. Then state how many decimal places the answer has.

Example 4

medium
A wire is 2.42.4 m long and weighs 0.50.5 kg per meter. Find the total weight.

Example 5

medium
Multiply: 0.6×1.5×0.10.6 \times 1.5 \times 0.1.

Example 6

hard
Without long multiplication, find 1.5×0.6×41.5 \times 0.6 \times 4.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Calculate 0.6×50.6 \times 5.

Example 2

medium
Calculate 1.5×0.81.5 \times 0.8.

Example 3

easy
Multiply: 0.2×30.2 \times 3.

Example 4

easy
Multiply: 0.3×0.40.3 \times 0.4.

Example 5

easy
Multiply: 1.5×21.5 \times 2.

Example 6

easy
Multiply: 0.5×0.50.5 \times 0.5.

Example 7

easy
Multiply: 0.1×0.10.1 \times 0.1.

Example 8

easy
Multiply: 2.0×0.52.0 \times 0.5.

Example 9

easy
Multiply: 0.6×100.6 \times 10.

Example 10

easy
Multiply: 0.4×20.4 \times 2.

Example 11

medium
Multiply: 1.2×0.31.2 \times 0.3.

Example 12

medium
Multiply: 1.2×0.031.2 \times 0.03.

Example 13

medium
Multiply: 2.5×1.42.5 \times 1.4.

Example 14

medium
A notebook costs $1.25\$1.25. How much for 44 notebooks?

Example 15

medium
Multiply: 0.25×0.40.25 \times 0.4.

Example 16

medium
Multiply: 3.14×23.14 \times 2.

Example 17

medium
Multiply: 0.05×0.050.05 \times 0.05.

Example 18

medium
Multiply: 1.5×0.2×101.5 \times 0.2 \times 10.

Example 19

medium
Multiply: 4.2×1.54.2 \times 1.5.

Example 20

challenge
A wall is 3.53.5 m by 2.42.4 m. Paint costs $0.50\$0.50 per square meter. What is the total paint cost?

Example 21

challenge
Without computing the full product, how many decimal places does 0.012×0.00040.012 \times 0.0004 have, and what is the product?

Example 22

challenge
If a×b=0.18a \times b = 0.18 and a=0.6a = 0.6, find bb. Then state how many decimal places bb has.

Example 23

easy
Multiply: 0.7×40.7 \times 4.

Example 24

easy
Multiply: 0.9×0.20.9 \times 0.2.

Example 25

easy
Multiply: 0.02×50.02 \times 5.

Example 26

easy
Multiply: 1.1×1.11.1 \times 1.1.

Example 27

medium
Multiply: 3.6×2.53.6 \times 2.5.

Example 28

medium
Multiply: 0.45×0.20.45 \times 0.2.

Example 29

medium
Multiply: 1.25×0.81.25 \times 0.8.

Example 30

medium
Multiply: 0.75×0.40.75 \times 0.4.

Example 31

medium
Multiply: 6.3×0.046.3 \times 0.04.

Example 32

medium
A bottle of juice costs $2.75\$2.75. How much for 66 bottles?

Example 33

medium
Multiply: 0.12×0.120.12 \times 0.12.

Example 34

hard
Multiply: 2.4×3.752.4 \times 3.75.

Example 35

hard
A rectangular garden is 4.54.5 m by 3.63.6 m. Compute its area to one decimal place.

Example 36

hard
Multiply: 0.005×0.040.005 \times 0.04.

Example 37

hard
If you double 0.350.35 and then multiply by 0.50.5, what is the result?

Example 38

hard
Compute 0.125×160.125 \times 16.

Example 39

challenge
A tile is 0.150.15 m by 0.150.15 m. How many tiles cover a 33 m by 4.54.5 m floor exactly?

Example 40

challenge
A cubical box has side 0.20.2 m. What is its volume in cubic meters and how many decimal places does the answer have?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

multiplicationplace value