Multiplying Decimal Numbers

The technique to use to multiply decimal numbers depends on how they are written: whether in decimal form or as fractions.

I. When the numbers are written in decimal form

To find the product of the two numbers 5.23 and 41.8 in decimal form, we just need to set up the multiplication in the same way as we would for whole numbers:

Then we carry out the multiplication, ignoring the decimal points:

Next we count up how many digits there are altogether after the decimal points in the two factors: In this case, there are three (the 2, the 3, and the 8). So there must be three digits after the decimal point in the answer.

We find: 5.23 × 41.8 = 218.614.

II. When the numbers are written as fractions

We want to express the result of the multiplication of two decimal numbers using a decimal fraction.


To do this, we just need to use the following rule: The product of two fractions is a fraction where the numerator is the product of the two numerators and the denominator is the product of the two denominators.


For example:  $\frac{47}{10}\times \frac{107}{100}=\frac{47\times 107}{10\times 100}=\frac{5029}{1000}$

Note: It is possible to write the fractions in decimal form in order to find the result.
Thus, $\frac{47}{10}\times \frac{107}{100}=4.7\times 1.07$ ; then we proceed as above, and get the result 5.029, which can also be written as $\frac{5029}{1000}$ .

Read more:
Reading and Writing Decimal Numbers
Multiplying or Dividing a Decimal Number by 10, 100, or 1,000
Dividing Decimal Numbers
Converting Decimals to Fractions
The Effect of Addition and Multiplication on the Order of Numbers
Describing Different Types of Numbers
Dividing Whole Numbers with a Remainder
Comparing and Ordering Decimal Numbers
Adding and Subtracting Decimal Numbers