How to Multiply Numbers with Decimals

This is the third part of the Operations on Decimals Series and in this post, we discuss about Multiplication of Decimals. In multiplying decimals, the decimal point in the product has something to do with the number of decimals of the factors.

How to Multiply Numbers with Decimals Examples

Example 1:  What is  3.6 \times 4?

In this example, only one factor has a decimal number, the other is a whole number. To multiply, first, ignore the decimal point and then just multiply the numbers:

36 \times 4 = 144.

After multiplying, count the number of decimal numbers (numbers after on the right hand side of the decimal point) of the factors. There is only one decimal number which is 6. So, in the product, starting from the right, count one number and then place the decimal point before that number making it 14.4.

So, the final answer is 14.4.

Example 2: What is 8.3 \times 4.2?

Again, ignore the decimal points and multiply the numbers:

83 \times 42 = 3486.

There is one decimal number in the first factor and one in the second factor. Therefore, there are two decimal numbers. Now, count two numbers from the right, and place the decimal point before the last number on your count.

Therefore, the correct answer is 34.86.

Example 3: What is 3.28 \times 0.01?

Now, 328 \times 1 = 328. Notice that there are only three numbers in the product, but there are four decimal numbers in the two factors. So, in the product, we count three numbers from the right hand side and then add one 0 before 3 to make the number of decimals four. So, the correct answer is .0328 or 0.0328.

Multiplying Decimal Numbers by 10

In multiplying decimal numbers by 10 or its powers, just count the number of zeroes and move the decimal point to the right hand side the number of zeroes appear.

Example 1: What is 3.45 \times 10?

Ten has one zero, so, we move the decimal point one place to the right hand side. Therefore, the correct answer is 34.5.

Example 2: What is 76.98301 \times 100?

There are two zeros, so we move the decimal point two digits to the right hand side. Moving the decimal points gives us 7698.301

Example 3: What is 34.7 \times 1000?

There are three zeros, however, only one decimal point. So, we move the decimal point one time to the right of seven, and add two zeros. Therefore, the final answer is 34700.

In the next post, we will be discussing about division of decimal numbers.

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