Rule for Multiplying Decimals

When multiplying decimals, the process is similar to multiplying whole numbers, but we must account for the placement of the decimal point in the final product. Here’s a step-by-step explanation.

Step 1: Ignore the Decimals and Multiply Normally

First, multiply the numbers as if they were whole numbers, ignoring the decimal points.

Step 2: Count the Total Number of Decimal Places

Count the total number of decimal places in the numbers being multiplied. This is the total number of digits to the right of the decimal points in both numbers.

Step 3: Place the Decimal Point in the Product

In the product (result), place the decimal point so that it has the same number of decimal places as the total counted in Step 2.

Step 4: Simplify if Necessary

If the product can be simplified (like removing trailing zeros), do so.

Example 1: Multiplying 3.2 by 2.5

1. Ignore the Decimals: Multiply 32 by 25 as if they are whole numbers.
2. 32 × 25 = 800
3. Count Decimal Places: 3.2 has one decimal place, and 2.5 has one decimal place. So, the total number of decimal places is 2.
4. Place the Decimal Point: Starting from the right of the product, place the decimal point two places to the left: 800→8.00
5. So, the product of 3.2 and 2.5 is 8.00, or simply 8.

Example 2: Multiplying 4.56 by 0.3

1. Ignore the Decimals: Multiply 456 by 3.
2. 456 x 3 = 1368
3. Count Decimal Places: 4.56 has two decimal places, and 0.3 has one decimal place. So, the total number of decimal places is 3.
4. Place the Decimal Point: Place the decimal point three places from the right:1368→1.368 So, the product of 4.56 and 0.3 is 1.368.

Example 3: Multiplying 0.25 by 0.04

1. Ignore the Decimals: Multiply 25 by 4.
2. 25 x 4 = 100
3. Count Decimal Places: 0.25 has two decimal places, and 0.04 has two decimal places. So, the total number of decimal places is 4.
4. Place the Decimal Point: Place the decimal point four places from the right:100→0.0100
5. So, the product of 0.25 and 0.04 is 0.0100, or simply 0.01.

Summary

• Multiply the numbers as if they were whole numbers.
• Count the total number of decimal places in the original numbers.
• Place the decimal point in the product so that the total number of decimal places matches the count.
• Simplify the product if necessary.

This rule ensures we correctly multiply decimals and place the decimal point accurately in the final product.