Multiplying Decimals Lesson: Rules, Examples, and Problems

Lesson Overview

• What Are Decimals?
• Rules for Multiplying Decimals
• Step-by-Step Examples
• Decimal Multiplication Table
• Word Problem
• Decimal Place Reference Table
• Helpful Tips
• Common Mistakes and How to Avoid Them

Multiplying decimals is an important math skill that is used in everyday life. You use it when shopping, measuring ingredients in a recipe, calculating money, and much more. Even though decimal multiplication might seem tricky at first, it follows simple rules. The key is knowing how to multiply numbers and where to place the decimal in the final answer. This lesson will guide you through the steps with helpful examples, word problems, and tips.

What Are Decimals?

Decimals are numbers that include a decimal point. This point separates the whole number part from the fractional part. For example:

• 3.2 means three and two-tenths
• 6.45 means six and forty-five hundredths
• 0.07 means seven hundredths

Each digit after the decimal point has a specific place value:

Rules for Multiplying Decimals

Multiplying decimals follows three main steps:

1. Ignore the decimal point and multiply the numbers like whole numbers.
2. Count all the decimal digits in both original numbers.
3. Place the decimal in the product by moving it from right to left based on the total number of decimal digits.

This method works whether you are multiplying two decimals or a decimal with a whole number.

Step-by-Step Examples

Let's walk through different examples to understand the process better.

Example 1: Multiply 3.2 × 1.5

Step 1: Ignore the decimals → 32 × 15 = 480
Step 2: Count decimal digits → 1 (from 3.2) + 1 (from 1.5) = 2
Step 3: Move the decimal two places → 4.80

Answer: 3.2 × 1.5 = 4.80

Example 2: Multiply 0.3 × 0.6

Step 1: Multiply 3 × 6 = 18
Step 2: Decimal digits = 1 (from 0.3) + 1 (from 0.6) = 2
Step 3: Move decimal two places → 0.18

Answer: 0.3 × 0.6 = 0.18

Example 3: Multiply 5.75 × 0.4

Step 1: Multiply 575 × 4 = 2300
Step 2: Decimal digits = 2 (from 5.75) + 1 (from 0.4) = 3
Step 3: Move decimal three places → 2.300

Answer: 5.75 × 0.4 = 2.300 (or 2.3)

Example 4: Multiply 6 × 0.05

Step 1: Multiply 6 × 5 = 30
Step 2: Decimal digits = 2 (from 0.05)
Step 3: Move decimal two places → 0.30

Answer: 6 × 0.05 = 0.30 (or 0.3)

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Multiplying And Dividing Decimals Quiz

Decimal Multiplication Table

This table shows different examples of multiplying decimals using the method described.

Word Problem

Example 1: You bought 3 notebooks. Each notebook costs $2.35. What is the total cost?

Step 1: Multiply 235 × 3 = 705
Step 2: Decimal digits = 2 (from 2.35)
Step 3: Final answer = 7.05

You paid $7.05 for 3 notebooks.

Example 2: A bottle holds 1.25 liters of water. If you have 4 bottles, how much water is that in total?

Step 1: Multiply 125 × 4 = 500
Step 2: Decimal digits = 2
Step 3: Final answer = 5.00 liters

The total is 5.00 liters of water.

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Multiplying Decimals Practice VIDA

Decimal Place Reference Table

This table shows how to count decimal digits before placing the decimal point in the final answer.

Helpful Tips

• Multiply first, place the decimal at the end.
• Count all decimal digits in the original numbers.
• Don't round off until the final answer.
• Estimate the answer before you solve to check if it makes sense.

Common Mistakes and How to Avoid Them

By practicing these steps regularly, you will become more confident in multiplying decimals in both number problems and real-life situations. This is a skill that will help you in higher-level math and in solving daily problems involving money, measurements, and quantities.

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Multiplying Decimals