Multiplication of decimals worksheets: Multiplication of Decimals Worksheets | K5 Learning

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Multiply decimals by powers of 10 Worksheets for Kids

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Multiply decimals by whole numbers Worksheets for Kids

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Multiply decimals by decimals Worksheets for Kids

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Multiply Decimals
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Multiplying Decimals Worksheets — Math Worksheets

Check out these free decimal worksheets.  Designed as a progressive practice series, these worksheets introduce basic decimal multiplication in the beginning, and then encourage your children to practice multiplying a variety of different decimal places in a variety of different ways.

Each set of problems becomes progressively more complicated, as students move from multiplying one digit numbers to two and three-digit numbers.  Your children will learn how to use zero as holder of place values and how to multiply both horizontally and vertically.

Each math worksheet features an answer key as well as examples that illustrate how to solve the exercises.  The practice problems feature plenty of space to show your work and area easily customized.   From hundredths to thousandths, the exercises on this page will help you practice multiplying a variety of decimals in variety of ways.

Online Practice Multiplying Decimals 1 – Save paper and practice decimal multiplication with the awesome imathworksheet. Click below for free online decimal multiplication practice. You can even print results or embed this worksheet on your website.
Online Practice Multiplying Decimals 1 | imathworksheet

Online Practice Multiplying Decimals 2 –
Online Practice Multiplying Decimals 2 | imathworksheet

Multiplying Decimals Worksheet 1 – Here is a twenty problem worksheet featuring decimal multiplication.  You will be multiplying by a single digit number, which will help you focus on correctly placing the decimal point in your answer.
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Multiplying Decimals Worksheet 2 – This is another twenty problem worksheet featuring decimal multiplication.   You will be multiplying by a single digit number, which will help you focus on correctly placing the decimal point in your answer.
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Multiplying Decimals Worksheet 3 – Here is a twenty problem worksheet featuring decimal multiplication.  You will be multiplying by a two digit number, which means there will be two rows of numbers to add up before calculating your answer.
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Multiplying Decimals Worksheet 4 – This is another twenty problem worksheet featuring decimal multiplication.  You will be multiplying by a two digit number, which means there will be two rows of numbers to add up before calculating your answer.
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Multiplying Decimals Worksheet 5 – Here is a twenty problem worksheet featuring decimal multiplication.  You will be multiplying by a three digit number, which means there will be three rows of numbers to add up before calculating your answer.
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Multiplying Decimals Worksheet 6 – This is another twenty problem worksheet featuring decimal multiplication.  You will be multiplying by a three digit number, which means there will be two rows of numbers to add up before calculating your answer.
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rules, examples, solutions, how to multiply decimal fractions

In this article we will consider such an action as multiplying decimal fractions. Let’s start with the formulation of general principles, then we will show how to multiply one decimal fraction by another and consider the method of multiplication by a column. All definitions will be illustrated with examples. Then we will analyze how to correctly multiply decimal fractions by ordinary, as well as by mixed and natural numbers (including 100, 10, etc.)

Within the framework of this material, we will only touch on the rules for multiplying positive fractions. Cases with negative numbers are discussed separately in the articles on the multiplication of rational and real numbers.

Multiplication of decimal fractions: general principles

Let’s formulate the general principles that must be followed when solving problems of multiplying decimal fractions.

Let us first recall that decimal fractions are nothing but a special form of writing ordinary fractions, therefore, the process of their multiplication can be reduced to the same for ordinary fractions. This rule works for both finite and infinite fractions: after converting them to ordinary fractions, it is easy to perform multiplication with them according to the rules we have already studied.

Let’s see how such problems are solved.

Example 1

Calculate the product of 1.5 and 0.75.

Solution: First, let’s replace decimal fractions with ordinary ones. We know that 0.75 is 75/100 and 1.5 is 1510. We can reduce the fraction and extract the whole part. We will write the result 1251000 as 1.125.

Answer: 1.125.

We can use the column counting method, just like for natural numbers.

Example 2

Multiply one periodic fraction 0,(3) by another 2,(36).

Solution

First, let’s reduce the initial fractions to ordinary ones. We get:

0,(3)=0.3+0.03+0.003+0.003+…=0.31-0.1=0.39=39=132,(36)=2+ 0.36+0.0036+…=2+0.361-0.01=2+3699=2+411=2411=2611

Therefore, 0,(3) 2,(36)=13 2611 =2633.

The resulting ordinary fraction can be reduced to a decimal form by dividing the numerator by the denominator in a column:

Answer: 0, (3) 2, (36) \u003d 0, (78).

If we have infinite non-periodic fractions in the condition of the problem, then we need to perform their preliminary rounding (see the article on rounding numbers if you forgot how to do this). After that, you can perform the multiplication operation with already rounded decimal fractions. Let’s take an example.

Example 3

Calculate the product of 5.382… and 0.2.

Solution

We have an infinite fraction in the problem, which must first be rounded to hundredths. It turns out that 5.382 … ≈5.38. Rounding the second factor to hundredths does not make sense. Now you can calculate the desired product and write down the answer: 5.38 0.2=538100 210=1 0761000=1.076.

Answer: 5.382… 0.2≈1.076.

How to multiply decimals by a column

The column counting method can be used not only for natural numbers. If we have decimals, we can multiply them in exactly the same way. Let’s derive the rule:

Definition 1

Multiplication of decimal fractions by a column is performed in 2 steps:

1. Perform multiplication by a column, not paying attention to commas.

2. We put a decimal point in the final number, separating it as many digits on the right side as both factors contain decimal places together. If as a result there are not enough numbers for this, we add zeros on the left.

Let’s analyze examples of such calculations in practice.

Example 4

Multiply the decimals 63.37 and 0.12 by a column.

Solution

Let’s do the multiplication first, ignoring the decimal points.

Now we need to put the comma in the right place. It will separate four digits on the right side, since the sum of the decimal places in both factors is 4. You don’t have to add zeros, because characters enough:

Answer: 3.37 0.12=7.6044.

Example 5

Calculate 3.2601 times 0.0254.

Solution

We count without commas. We get the following number:

We will put a comma separating 8 digits on the right side, because the original fractions together have 8 decimal places. But our result has only seven digits, and we cannot do without additional zeros:

Answer: 3.2601 0.0254=0.08280654.

How to multiply decimals by 0.001, 0.01, 01, etc.

Multiplying decimals by such numbers is a common practice, so it is important to be able to do it quickly and accurately. Let’s write down a special rule that we will use in this multiplication:

Definition 2

If we multiply a decimal fraction by 0.1, 0.01, etc., we end up with a number similar to the original fraction, the comma of which has been moved to the left by the required number of characters. If there are not enough digits to transfer, you need to add zeros on the left.

So, to multiply 45.34 by 0.1, you need to move the comma in the original decimal fraction by one digit. We will end up with 4,534.

Example 6

Multiply 9.4 by 0.0001.

Solution

We will have to move the comma to four digits according to the number of zeros in the second factor, but there are not enough digits in the first one. We assign the necessary zeros and get that 9.4 0.0001=0.00094.

Answer: 0.00094.

For infinite decimals, we use the same rule. So, for example, 0,(18) 0.01=0.00(18) or 94.938… 0.1=9.4938…. etc.

How to multiply a decimal fraction with a natural number

The process of such multiplication is no different from the multiplication of two decimal fractions. It is convenient to use the multiplication method in a column if the condition of the problem contains a final decimal fraction. In this case, it is necessary to take into account all the rules that we talked about in the previous paragraph.

Example 7

Calculate how much 15 2.27 will be.

Solution

Multiply the original numbers by a column and separate two commas.

Answer: 15 2.27 = 34.05.

If we are multiplying a periodic decimal fraction by a natural number, we must first change the decimal fraction to an ordinary one.

Example 8

Calculate the product of 0,(42) and 22.

Solution

Let’s reduce the periodic fraction to the ordinary form.

0,(42)=0.42+0.0042+0.000042+…=0.421-0.01=0.420.99=4299=1433

Then we multiply:

0.42 22=1433 22=14 223=283=913

We can write the final result as a periodic decimal fraction as 9,(3).

Answer: 0,(42) 22=9,(3).

Infinite fractions must be rounded before counting.

Example 9

Calculate how much is 4 2.145….

Solution

Round off the original infinite decimal to hundredths. After that, we will come to the multiplication of a natural number and a final decimal fraction:

4 2.145…≈4 2.15=8.60.

Answer: 4 2.145…≈8.60.

How to multiply a decimal by 1000, 100, 10, etc.

Multiplying a decimal by 10, 100, etc. is often found in problems, so we will analyze this case separately. The basic multiplication rule is:

Definition 3

To multiply a decimal by 1000, 100, 10, etc. , you need to move its comma by 3, 2.1 digits depending on the multiplier and discard extra zeros on the left. If there are not enough digits to move the comma, we add as many zeros to the right as we need.

Let’s show on an example how exactly to do it.

Example 10

Multiply 100 and 0.0783.

Solution

To do this, we need to move the decimal point by 2 digits to the right side. We end up with 007.83 The zeros on the left can be discarded and the result written as 7.38.

Answer: 0.0783 100=7.83.

Example 11

Multiply 0.02 by 10 thousand.

Solution: we will move the comma four digits to the right. In the original decimal fraction, we do not have enough signs for this, so we have to add zeros. In this case, three 0s will be enough. As a result, we got 0.02000, we move the comma and get 00200.0. Ignoring the zeros on the left, we can write the answer as 200.

Answer: 0. 02 10 000=200.

The rule we have given will work in the same way in the case of infinite decimal fractions, but here one should be very attentive to the period of the final fraction, since it is easy to make a mistake in it.

Example 12

Calculate the product of 5.32(672) times 1,000.

Solution: First of all, we write the periodic fraction as 5.32672672672…, so there will be less chance of making a mistake. After that, we can move the comma to the desired number of characters (three). As a result, we get 5326.726726 … Let’s put the period in brackets and write the answer as 5326.726.

Answer: 5.32(672) 1000=5326.(726).

If in the conditions of the problem there are infinite non-periodic fractions that must be multiplied by ten, one hundred, one thousand, etc., do not forget to round them before multiplying.

How to multiply a decimal fraction with a common or mixed number

To perform this type of multiplication, you need to represent the decimal fraction as a common fraction and then follow the already familiar rules.

Example 13

Multiply 0.4 by 356

Solution

We have: 0.4=410=25.

Further we consider: 0.4 356=25 236=2315=1815.

We got a mixed number. You can write it as a periodic fraction 1.5(3).

Answer: 1.5(3).

If an infinite non-periodic fraction is involved in the calculation, you need to round it up to a certain figure and only then multiply it.

Example 14

Compute the product 3.5678… 23

Solution

We can represent the second factor as 23=0.6666…. Next, we round both factors to the thousandth place. After that, we will need to calculate the product of two final decimal fractions 3.568 and 0.667. Let’s count in a column and get the answer:

The final result must be rounded to thousandths, since it was to this category that we rounded the original numbers. We get that 2.379856≈2.380.

Answer: 3. 5678… 23≈2.380

MULTIPLICATION AND DIVISION OF DECIMAL FRACTIONS

P 34. Multiplication of decimal fractions by natural numbers

Let the field have the shape of a square with a side of 1.83 km. Let’s find the perimeter of the field: 1.85+1.85+1.85+1.85=7.32 km. To solve the problem, we found the sum of four terms, each of which is equal to 1.83. Such a sum is called the product of the number 1.83 and the natural number 4 and is denoted as 1.83∙4.

The product of a decimal fraction and a natural number is the sum of terms, each of which is equal to this fraction, and the number of terms is equal to this natural number.

The value 7.32 for the product 1.83∙4 can be obtained in another way: multiply 1.83 by 4, without paying attention to the comma, and in the resulting product 732, separate as many digits on the right with a comma as there are after the decimal point in the fraction 1, 83:


2) in the resulting product, separate with a comma as many digits on the right as there are separated by a comma in a decimal fraction.

Find the product 9.865∙10. According to the rule, first we multiply 9865 by 10, we get 9865∙10=9865. Now we separate the three digits on the right with a comma and get:

9.865∙10=98.650=98.65

Thus, when multiplying 9.865 by 10, we move the comma through one digit to the right. If we multiply 9.865 by 100, we get 986.5, that is, the comma was moved two digits to the right. 9


P.35 Division of decimal fractions by natural numbers

Problem . A piece of tape 19.2 m long was cut into 8 equal parts. Find the length of each piece.

Solution . To solve the problem, we express the length of the tape in decimeters: 19.2 m = 192 dm. But 192: 8 = 24. This means that the length of each part is 24 dm, that is, 2.4 m. If we multiply 2.4 by 8, we get 19.2. So 2.4 is the quotient of 19.2 divided by 8.
They write: 19.2: 8 = 2.4.
The same answer can be obtained without converting meters to decimeters. To do this, divide 19.2 by 8, ignoring the comma, and put in a private comma when the division of the integer part ends:

gives the dividend to this natural number.

To divide a decimal fraction by a natural number , you must:
1) divide the fraction by this number, do not pay attention to the comma;
2) put a comma in the quotient when the division of the integer part is over.

If the integer part is less than the divisor, then the quotient starts from zero integers:

Divide 96.1 by 10. If you multiply the quotient by 10, you should get 96.1 again.
But when multiplying a decimal fraction by 10, the decimal point is moved one digit to the right. So, when dividing by 10, the comma must be moved one digit to the left: 96.1 : 10 = 9.61.
Verification: 9.61 . 10 = 96.1.
When dividing by 100, the comma is moved two digits to the left.

To divide a decimal fraction by 10, 100, 1000 and so on, you need to move the comma in this fraction as many digits to the left as there are zeros in the divisor after one.