How to Multiply Decimals?

Multiplying decimals is a mathematical operation that involves multiplying numbers with decimal points.

Imagine a scenario where you’re dealing with measurements that aren’t just whole units but also include fractional parts, or picture a situation where you need to calculate the total cost of items with prices that extend beyond whole dollars.

In real-life situations, multiplying decimals helps you find precise solutions to a wide range of problems.

Multiplying Decimals with Whole Numbers

Multiplying decimals with whole numbers is like multiplying whole numbers but involves an additional consideration for decimal places. Here are the key differences and steps when multiplying decimals with whole numbers compared to multiplying whole numbers:

Step 1: Multiply as if Whole Numbers

Treat the decimal number as if it were a whole number and multiply it by the whole number just as you would with two whole numbers.

Example

  3.2

x   5

—–

160   (32 multiplied by 5)

Step 2: Adjust the Decimal Point

Count the decimal places in the decimal number (3.2, in this case, has one decimal place). This number will indicate how many decimal places the final product should have.

Place the decimal point in the product by counting from the right of the result, starting with the last digit. Count as many decimal places as you counted in Step 2.

  3.2

X   5

—–

  16.0   (Final product with one decimal place)

Always keep in mind that the product after multiplication must have the same number of decimal places as the factors.

Multiplying Two Decimal Numbers

Example: Multiply 2.4 by 0.6.

Step 1: Multiply as if Whole Numbers

Treat both decimal numbers as if they were whole numbers. Multiply them just as you would with two whole numbers, ignoring the decimal points for now.

  2.4

x 0.6

—–

  144   (24 multiplied by 6)

Step 2: Adjust the Decimal Places

Count the number of decimal places in both decimal numbers (2.4 has one decimal place, and 0.6 has one decimal place).

The total number of decimal places in the product should be the sum of the decimal places in the original numbers (1 + 1 = 2).

Step 3: Place the Decimal Point

Place the decimal point in the product by counting from the right, starting at the end of the result. Count the number of decimal places you determined in Step 2.

  2.4

x 0.6

—–

  1.44   (Final product with two decimal places)

Multiplying Decimals by 10, 100 and 1000

Multiplying decimals by powers of 10, such as 10, 100, and 1000, is a straightforward process that involves shifting the decimal point to the right by the number of positions corresponding to the number of zeros in the power of 10.

Here are the rules for multiplying decimals by 10, 100, and 1000:

Example: Multiply 3.75 X 10 = 37.5

• If we multiply any decimal by 100, we shift the decimal point two places towards the right.

Example: Multiply 2.68 X 100 = 268.00 or 268

• Similarly, if we multiply a decimal by 1000, we shift the decimal point by three places towards the right, and so on.

Example: Multiply 0.43 X 1000 = 430.00 or 430

Important Notes:

Here are some important notes related to the concept of multiplying decimals.

1. When multiplying decimals, always pay attention to the place value of each digit, especially when shifting the decimal point.
2. When you multiply a decimal by a power of 10 (10, 100, 1000, etc.), the decimal point shifts to the right by the same number of places as the exponent of the power of 10. This results in the value being scaled up by that power of 10.
3. When multiplying decimals, if there’s a zero to the right of the decimal point in one of the factors, you can often omit it during multiplication since it doesn’t affect the result. For example, 2.5 * 0.6 is the same as 2.5 * 6.
4. When determining the number of decimal places in the product, count the total number of decimal places in the multiplied numbers. It will tell you where the decimal point should be placed in the final answer.
5. If the product has more decimal places than the number of digits, zeros can be inserted on the left before placing the decimal point in the product.
6. The order of multiplication does not affect the result when multiplying decimals. For example, 3.2 * 4.5 is the same as 4.5 * 3.2.

Order of Operations FAQS

Grade 6 Science Worksheets

• Inquiry process
• Nature of Science
• Scientific Inquiry
• Inquiry, Analysis and Problem Solving
• Ethical Practices
• Science and Society
• Biotic and Abiotic Factors
• Impact of Organisms
• Adaptation
• Spheres of Earth
• Natural Resources
• Environmental Issues
• Conservation of Earth
• Understanding Technology
• Abilities To Do Technological Design
• Structure of Earth
• Solar System
• Rocks and Fossils
• Earth Systems
• Plate Tectonics
• Evolution
• Magnetic Field of Earth
• Geologic Time
• Materials and Processes That Shape a Planet
• Astronomy
• Ecology
• Energy
• Kinetic and Potential Energy
• Energy Transfer
• Matter and its Structure
• States of Matter
• Physical and Chemical Changes
• Force and Motion
• Electricity and Magnetism
• Wave Interactions
• Sound
• Light
• Introduction to Life Science
• The Origin & History of Life On Earth
• Plant and Animal Cells
• Parts of a Cell
• The Cell Cycle
• How Living Organisms Get Energy
• Classification of Organisms
• How Plants Grow & Reproduce
• The Human Respiratory System
• The Human Cardiovascular System
• The Human Digestive System
• The Human Endocrine Systems
• The Human Nervous System
• The Human Muscular System
• The Human Skeletal System

Grade 6 Math Worksheets

• Probability
• Ratio
• Sequence & Patterns
• Division Word Problems  (New)
• Solving two step equations (New)
• One Step Equation  (New)
• Place Value  (New)
• Two Step Equation  (New)
• To convert percents to decimals and vice versa  (New)
• To convert Percents to Fractions and vice versa  (New)