Back forward

Attention! Slide previews are for informational purposes only and may not represent all the presentation options. If you are interested in this work, please download the full version.

The purpose of the lesson:

• Introduce to students in a fun form the rule for multiplying a decimal fraction by a natural number, by a digit unit and the rule for expressing a decimal fraction as a percentage. Develop the ability to apply the knowledge gained when solving examples and problems.
• To develop and activate the logical thinking of students, the ability to identify patterns and generalize them, strengthen memory, the ability to cooperate, provide assistance, evaluate their work and the work of each other.
• To foster interest in mathematics, activity, mobility, the ability to communicate.

Equipment: interactive whiteboard, poster with cyphergram, posters with statements of mathematicians.

During the classes

1. Organizing time.
2. Oral counting is a generalization of previously studied material, preparation for the study of new material.
3. Explanation of the new material.
4. Home assignment.
5. Mathematical physical education minute.
6. Generalization and systematization of the knowledge gained in game form using a computer.
7. Grading.

2. Guys, today our lesson will be somewhat unusual, because I will not teach it alone, but with my friend. And my friend is also unusual, now you will see him. (A cartoon computer appears on the screen.) My friend has a name and can speak. What's your name, buddy? Komposha replies: "My name is Komposha." Are you ready to help me today? YES! Well then, let's start the lesson.

Today I received an encrypted cyphergram, guys, which we must solve and decipher together. (A poster with oral counting for addition and subtraction is posted on the board. decimal fractions, as a result of which the guys get the following code 523914687. )

Composha helps to decipher the received code. As a result of decoding, the word MULTIPLICATION is obtained. Multiplication is keyword topics of today's lesson. The topic of the lesson is displayed on the monitor: "Multiplying a decimal fraction by a natural number"

Guys, we know how the multiplication of natural numbers is performed. Today we will look at multiplication decimal numbers by a natural number. The multiplication of a decimal fraction by a natural number can be considered as the sum of terms, each of which is equal to this decimal fraction, and the number of terms is equal to this natural number. For example: 5.21 3 = 5.21 + 5.11 + 5.21 = 15.63 Hence, 5.21 3 = 15.63. Representing 5.21 as an ordinary fraction by a natural number, we get

And in this case we got the same result 15.63. Now, disregarding the comma, we take the number 521 instead of the number 5.21 and multiply it by this natural number. Here we must remember that in one of the factors, the comma has been moved two places to the right. When multiplying the numbers 5, 21 and 3, we get the product equal to 15.63. Now, in this example, we will move the comma to the left by two places. Thus, by how many times one of the factors was increased, the product was reduced by that many times. Based on the similarities of these methods, we draw a conclusion.

To multiply a decimal fraction by a natural number, you need:
1) ignoring the comma, perform the multiplication of natural numbers;
2) in the resulting product, separate with a comma on the right as many digits as there are in a decimal fraction.

The following examples are displayed on the monitor, which we analyze together with Kompoche and the guys: 5.21 · 3 = 15.63 and 7.624 · 15 = 114.34. Then I show the multiplication by the round number 12.6 50 = 630. Next, I turn to multiplying the decimal fraction by the digit unit. I show the following examples: 7,423 · 100 = 742.3 and 5.2 · 1000 = 5200. So, I introduce the rule for multiplying a decimal fraction by a digit unit:

To multiply a decimal fraction by 10, 100, 1000, etc., you need to move the comma to the right in this fraction by as many digits as there are zeros in the bit unit record.

I end the explanation with a decimal percentage. I introduce the rule:

To express a decimal fraction as a percentage, you need to multiply it by 100 and assign a% sign.

I give an example on a computer 0.5 · 100 = 50 or 0.5 = 50%.

4. At the end of the explanation, I give the guys homework, which is also displayed on the computer monitor: № 1030, № 1034, № 1032.

5. In order for the guys to have a little rest, to consolidate the topic, we do a mathematical physical education together with Komposha. Everyone stands up, I show the class solved examples and they must answer whether the example was solved correctly or not. If the example is correct, then they raise their hands above their heads and clap their palms. If the example is not solved correctly, the guys stretch their arms to the sides and knead their fingers.

6. And now you have a little rest, you can solve the tasks. Open the tutorial to page 205, № 1029. in this task, you need to calculate the value of the expressions:

The tasks appear on the computer. As they are solved, a picture appears with the image of a boat, which, when fully assembled, floats away.

No. 1031 Calculate:

Solving this task on the computer, the rocket gradually develops, solving the last example, the rocket flies away. The teacher gives a little information to the students: “Every year from the Kazakh land from the Baikonur cosmodrome, spaceships take off to the stars. Kazakhstan is building its new Baiterek cosmodrome near Baikonur.

No. 1035. Problem.

What is the distance a passenger car will cover in 4 hours if the speed of a passenger car is 74.8 km / h.

This task is accompanied by sound design and a brief statement of the task on the monitor. If the problem is solved correctly, then the car begins to move forward to the finish flag.

№ 1033. Write down the decimals as percentages.

0,2 = 20%; 0,5 = 50%; 0,75 = 75%; 0,92 = 92%; 1,24 =1 24%; 3,5 = 350%; 5,61= 561%.

Solving each example, when the answer appears, a letter appears, resulting in the word Well done.

The teacher asks Komposhu, what would this word appear for? Komposha replies: "Well done, guys!" and says goodbye to everyone.

The teacher summarizes the lesson and gives marks.

In the last lesson, we learned how to add and subtract decimal fractions (see the lesson "Adding and subtracting decimal fractions"). At the same time, we appreciated how much easier the calculations are compared to the usual "two-level" fractions.

Unfortunately, this effect does not occur with multiplication and division of decimal fractions. In some cases, decimal notation of a number even complicates these operations.

First, let's introduce a new definition. We will meet with him quite often, and not only in this lesson.

The significant part of a number is everything between the first and last nonzero digit, including the ends. We are talking only about numbers, the decimal point is not taken into account.

The digits included in the significant part of the number are called significant digits. They can be repeated or even zero.

For example, consider several decimal fractions and write out the corresponding significant parts:

1. 91.25 → 9125 (significant digits: 9; 1; 2; 5);
2. 0.008241 → 8241 (significant digits: 8; 2; 4; 1);
3. 15.0075 → 150075 (significant digits: 1; 5; 0; 0; 7; 5);
4. 0.0304 → 304 (significant digits: 3; 0; 4);
5. 3000 → 3 (there is only one significant digit: 3).

Please note: the zeros inside the significant part of the number do not go anywhere. We have already encountered something similar when we learned to convert decimal fractions into ordinary ones (see the lesson "Decimal fractions").

This point is so important, and mistakes are made here so often that I will publish a test on this topic in the near future. Be sure to practice! And we, armed with the concept of the meaningful part, proceed, in fact, to the topic of the lesson.

Decimal multiplication

The multiplication operation consists of three consecutive steps:

1. For each fraction, write out the significant part. The result will be two ordinary integers - without any denominators and decimal points;
2. Multiply these numbers by any in a convenient way... Directly, if the numbers are small, or in columns. We get the significant part of the desired fraction;
3. Find out where and by how many digits the decimal point in the original fractions is shifted to obtain the corresponding significant part. Perform reverse shifts for the significant part obtained in the previous step.

Let me remind you once again that zeros on the sides of the significant part are never counted. Ignoring this rule leads to errors.

1. 0.28 12.5;
2. 6.3 * 1.08;
3. 132.5 * 0.0034;
4. 0.0108 * 1600.5;
5. 5.25 10,000.

We work with the first expression: 0.28 · 12.5.

1. Let's write out the significant parts for the numbers from this expression: 28 and 125;
2. Their product: 28 · 125 = 3500;
3. In the first multiplier, the decimal point is shifted by 2 digits to the right (0.28 → 28), and in the second - by 1 more digit. In total, a shift to the left by three digits is needed: 3500 → 3.500 = 3.5.

Now let's deal with the expression 6.3 · 1.08.

1. Let's write out the significant parts: 63 and 108;
2. Their product: 63 · 108 = 6804;
3. Again, two shifts to the right: by 2 and 1 digits, respectively. In total - again 3 digits to the right, so the reverse shift will be 3 digits to the left: 6804 → 6.804. This time there are no zeros at the end.

We got to the third expression: 132.5 · 0.0034.

1. Significant parts: 1325 and 34;
2. Their product: 1325 · 34 = 45,050;
3. In the first fraction, the decimal point goes to the right by 1 digit, and in the second - by whole 4. Total: 5 to the right. Shift 5 to the left: 45,050 →, 45050 = 0.4505. Zero was removed at the end, and added in front, so as not to leave a "bare" decimal point.

The following expression is 0.0108 1600.5.

1. We write the significant parts: 108 and 16 005;
2. We multiply them: 108 16 005 = 1 728 540;
3. We count the digits after the decimal point: in the first number there are 4, in the second - 1. In total - again 5. We have: 1,728 540 → 17.28540 = 17.2854. At the end, the "extra" zero was removed.

Finally, the last expression: 5.25 · 10,000.

1. Significant parts: 525 and 1;
2. We multiply them: 525 · 1 = 525;
3. The first fraction is shifted 2 digits to the right, and the second is shifted 4 digits to the left (10,000 → 1.0000 = 1). Total 4 - 2 = 2 digits to the left. We perform a reverse shift by 2 digits to the right: 525, → 52,500 (we had to add zeros).

Note the last example: as the decimal point moves to different directions, the total shift is found through the difference. This is very important point! Here's another example:

Consider the numbers 1.5 and 12,500. We have: 1.5 → 15 (shift by 1 to the right); 12,500 → 125 (shift 2 to the left). We "step" 1 digit to the right, and then 2 to the left. As a result, we stepped 2 - 1 = 1 digit to the left.

Division of decimal fractions

Division is perhaps the most difficult operation. Of course, here you can act by analogy with multiplication: divide the significant parts, and then "move" the decimal point. But in this case, there are many subtleties that negate the potential savings.

Therefore, let's consider a universal algorithm that is slightly longer, but much more reliable:

1. Convert all decimal fractions to common ones. With a little practice, this step will take you a matter of seconds;
2. Divide the resulting fractions in the classical way. In other words, multiply the first fraction by the "inverted" second (see the lesson "Multiplication and division of numeric fractions");
3. If possible, present the result as a decimal again. This step is also fast, because often the denominator is already a power of ten.

Task. Find the meaning of the expression:

1. 3,51: 3,9;
2. 1,47: 2,1;
3. 6,4: 25,6:
4. 0,0425: 2,5;
5. 0,25: 0,002.

We count the first expression. First, let's convert the obi fractions to decimal:

Let's do the same with the second expression. The numerator of the first fraction is again factorized:

There is an important point in the third and fourth examples: after getting rid of the decimal notation, cancellable fractions appear. However, we will not be implementing this reduction.

The last example is interesting because the numerator of the second fraction contains a prime number. There is simply nothing to factor out here, so we think ahead:

Sometimes, as a result of division, an integer is obtained (this is me about the last example). In this case, the third step is not performed at all.

In addition, division often produces "ugly" fractions that cannot be converted to decimal. This is how division differs from multiplication, where the results are always represented in decimal form. Of course, in this case, the last step is again not performed.

Note also the 3rd and 4th examples. In them, we deliberately do not abbreviate ordinary fractions derived from decimals. Otherwise, it will complicate the inverse problem - representing the final answer in decimal form again.

Remember: the basic property of a fraction (like any other rule in mathematics) in itself does not mean that it should be applied everywhere and always, at every opportunity.

In the middle and high school course, students studied the topic "Fractions". However, this concept is much broader than it is given in the learning process. Today, the concept of a fraction is encountered quite often, and not everyone can carry out calculations of any expression, for example, multiplication of fractions.

What is a fraction?

It so happened historically that fractional numbers appeared because of the need to measure. As practice shows, there are often examples of determining the length of a segment, the volume of a rectangular rectangle.

Initially, students are introduced to the concept of share. For example, if you divide a watermelon into 8 parts, then each will get one-eighth of the watermelon. This one part of the eight is called a fraction.

A fraction equal to ½ of any value is called half; ⅓ - third; ¼ - a quarter. Records of the form 5/8, 4/5, 2/4 are called ordinary fractions. A common fraction is divided into a numerator and a denominator. Between them is a fractional line, or fractional line. A slash can be drawn as either a horizontal or an oblique line. In this case, it denotes the division sign.

The denominator represents how many equal shares the value, the object is divided into; and the numerator is how many equal shares are taken. The numerator is written above the fractional line, the denominator below it.

It is most convenient to show ordinary fractions on the coordinate ray. If a unit segment is divided into 4 equal shares, each share is labeled with a Latin letter, then the result is an excellent visual aid. So, point A shows a fraction equal to 1/4 of the entire unit segment, and point B marks 2/8 of this segment.

Varieties of fractions

Fractions can be ordinary, decimal, and mixed numbers. In addition, fractions can be divided into correct and incorrect. This classification is more suitable for common fractions.

A correct fraction is understood as a number with the numerator less than the denominator... Respectively, improper fraction- a number whose numerator is greater than the denominator. The second kind is usually written as a mixed number. Such an expression consists of an integer and a fractional part. For example, 1½. 1 - whole part, ½ - fractional. However, if you need to carry out some manipulations with the expression (division or multiplication of fractions, their reduction or transformation), the mixed number is translated into an improper fraction.

A correct fractional expression is always less than one, and an incorrect one is always greater than or equal to 1.

As for that, this expression means a record in which any number is represented, the denominator of a fractional expression of which can be expressed through one with several zeros. If the fraction is correct, then the whole part in decimal notation will be equal to zero.

To write a decimal fraction, you must first write the whole part, separate it from the fractional part with a comma, and then write down the fractional expression. It must be remembered that after the comma, the numerator must contain the same number of digital characters as there are zeros in the denominator.

Example... Present the fraction 7 21/1000 in decimal notation.

Algorithm for converting an improper fraction to a mixed number and vice versa

It is incorrect to write an incorrect fraction in the answer of the problem, so it must be converted to a mixed number:

• divide the numerator by the existing denominator;
• v specific example incomplete quotient - whole;
• and the remainder is the numerator of the fractional part, and the denominator remains unchanged.

Example... Convert an improper fraction to a mixed number: 47/5.

Solution... 47: 5. The incomplete quotient equals 9, the remainder = 2. Hence, 47/5 = 9 2/5.

Sometimes you want to represent a mixed number as an improper fraction. Then you need to use the following algorithm:

• the integer part is multiplied by the denominator of the fractional expression;
• the resulting product is added to the numerator;
• the result is written in the numerator, the denominator remains unchanged.

Example... Provide a mixed number as an improper fraction: 9 8/10.

Solution... 9 x 10 + 8 = 90 + 8 = 98 - numerator.

Answer: 98 / 10.

Multiplication of ordinary fractions

Various algebraic operations can be performed on ordinary fractions. To multiply two numbers, multiply the numerator with the numerator, and the denominator with the denominator. Moreover, the multiplication of fractions with different denominators does not differ from the product fractional numbers with the same denominators.

It happens that after finding the result, you need to cancel the fraction. It is imperative to simplify the resulting expression as much as possible. Of course, one cannot say that an incorrect fraction in an answer is a mistake, but it is also difficult to call it a correct answer.

Example... Find the product of two ordinary fractions: ½ and 20/18.

As you can see from the example, after finding the work, we got an abbreviated fractional notation. Both the numerator and the denominator in this case are divided by 4, and the answer is 5/9.

Multiplication of decimal fractions

The product of decimal fractions is quite different from the product of ordinary ones in its principle. So, the multiplication of fractions is as follows:

• two decimal fractions must be written under each other so that the rightmost digits are one under the other;
• you need to multiply the written numbers, despite the commas, that is, as natural;
• count the number of digits after the comma in each of the numbers;
• in the result obtained after multiplication, you need to count as many digital symbols from the right as is contained in the sum in both factors after the decimal point, and put a separating sign;
• if there are fewer numbers in the product, then you need to write so many zeros in front of them to cover this amount, put a comma and assign the whole part equal to zero.

Example... Calculate the product of two decimal fractions: 2.25 and 3.6.

Solution.

Multiplication of mixed fractions

To calculate the product of two mixed fractions, you need to use the rule for multiplying fractions:

• Convert mixed numbers to improper fractions;
• find the product of the numerators;
• find the product of the denominators;
• write down the resulting result;
• Simplify the expression as much as possible.

Example... Find the product of 4½ and 6 2/5.

Multiplying a number by a fraction (fractions by a number)

In addition to finding the product of two fractions, mixed numbers, there are tasks where you need to multiply by a fraction.

So, to find the product of a decimal fraction and a natural number, you need:

• write the number under the fraction so that the rightmost digits are one above the other;
• find a work despite the comma;
• in the result obtained, separate the whole part from the fractional part using a comma, counting from the right the number of digits that is after the decimal point in the fraction.

To multiply common fraction by a number, you should find the product of the numerator and the natural factor. If the answer is a cancellable fraction, it should be converted.

Example... Calculate the product of 5/8 and 12.

Solution. 5 / 8 * 12 = (5*12) / 8 = 60 / 8 = 30 / 4 = 15 / 2 = 7 1 / 2.

Answer: 7 1 / 2.

As you can see from the previous example, it was necessary to shorten the resulting result and convert the incorrect fractional expression to a mixed number.

Also, the multiplication of fractions also applies to finding the product of a number in mixed form and a natural factor. To multiply these two numbers, you should multiply the integer part of the mixed factor by a number, multiply the numerator by the same value, and leave the denominator unchanged. If required, you need to simplify the resulting result as much as possible.

Example... Find the product of 9 5/6 and 9.

Solution... 9 5/6 x 9 = 9 x 9 + (5 x 9) / 6 = 81 + 45/6 = 81 + 7 3/6 = 88 1/2.

Answer: 88 1 / 2.

Multiplication by factors of 10, 100, 1000 or 0.1; 0.01; 0.001

The following rule follows from the previous paragraph. To multiply a decimal fraction by 10, 100, 1000, 10000, etc., you need to move the comma to the right by as many digits as there are zeros in the multiplier after one.

Example 1... Find the product of 0.065 and 1000.

Solution... 0.065 x 1000 = 0065 = 65.

Answer: 65.

Example 2... Find the product 3.9 and 1000.

Solution... 3.9 x 1000 = 3.900 x 1000 = 3900.

Answer: 3900.

If you need to multiply a natural number and 0.1; 0.01; 0.001; 0.0001, etc., you should move the comma to the left in the resulting product by as many digits as there are zeros up to one. If necessary, sufficient zeros are written in front of the natural number.

Example 1... Find the product of 56 and 0.01.

Solution... 56 x 0.01 = 0056 = 0.56.

Answer: 0,56.

Example 2... Find the product of 4 and 0.001.

Solution... 4 x 0.001 = 0004 = 0.004.

Answer: 0,004.

So, finding the product of different fractions should not cause any difficulties, except perhaps calculating the result; in this case, you simply cannot do without a calculator.

§ 1 Application of the rule of multiplication of decimal fractions

In this lesson, you will get acquainted and learn how to apply the rule for multiplying decimal fractions and the rule for multiplying a decimal fraction by a digit unit, such as 0.1, 0.01, etc. In addition, we will look at the properties of multiplication when finding the values ​​of expressions that contain decimal fractions.

Let's solve the problem:

The vehicle travels at a speed of 59.8 km / h.

Which way will the car cover in 1.3 hours?

As you know, to find a path, you need to multiply the speed by time, i.e. 59.8 times 1.3.

Let's write down the numbers in a column and start multiplying them, not noticing the commas: 8 multiplied by 3, it will be 24, 4 we write 2 in the mind, 3 multiplied by 9 is 27, and even plus 2, we get 29, we write 9, 2 in the mind. Now we multiply 3 by 5, it will be 15 and add 2 more, we get 17.

Go to the second line: 1 multiplied by 8, it will be 8, 1 multiplied by 9, we get 9, 1 multiplied by 5, we get 5, add these two lines, we get 4, 9 + 8 equals 17, 7 write 1 in our mind, 7 +9 is 16 and 1 more, it will be 17, 7 we write 1 in the mind, 1 + 5 and 1 more we get 7.

Now let's see how many decimal places are there in both decimal fractions! In the first fraction there is one digit after the decimal point and in the second fraction there is one digit after the decimal point, only two digits. This means that on the right in the resulting result, you need to count two digits and put a comma, i.e. will be 77.74. So, when you multiply 59.8 by 1.3, you get 77.74. So the answer in the problem is 77.74 km.

Thus, to multiply two decimal fractions, you need:

First: do the multiplication, ignoring the commas

Second: in the resulting product, separate as many digits on the right with a comma as there are after the comma in both factors together.

If there are fewer numbers in the resulting product than must be separated by a comma, then one or more zeros must be added in front.

For example: 0.145 multiplied by 0.03, we get 435 in the product, and we need to separate 5 digits from the right with a comma, so we add 2 more zeros in front of the number 4, put a comma and add one more zero. We get the answer 0.00435.

§ 2 Properties of multiplication of decimal fractions

When multiplying decimal fractions, all the same properties of multiplication are preserved as for natural numbers. Let's do a few tasks.

Task number 1:

Let's solve this example by applying the distribution property of multiplication to addition.

We put 5.7 (the common factor) outside the parenthesis, in parentheses there will be 3.4 plus 0.6. The value of this sum is 4, and now 4 must be multiplied by 5.7, we get 22.8.

Task number 2:

Let's apply the displacement property of multiplication.

First we multiply 2.5 by 4, we get 10 integers, and now we need to multiply 10 by 32.9 and we get 329.

In addition, when multiplying decimal fractions, you can notice the following:

When multiplying a number by an incorrect decimal, i.e. greater than or equal to 1, it increases or does not change, for example:

When multiplying a number by a correct decimal fraction, i.e. less than 1, it decreases, for example:

Let's solve an example:

23.45 times 0.1.

We have to multiply 2,345 by 1 and separate the three decimal places on the right to get 2.345.

Now let's solve another example: 23.45 divided by 10, we have to move the comma to the left by one digit, because 1 is a zero in a bit, we get 2.345.

From these two examples, we can conclude that multiplying the decimal fraction by 0.1, 0.01, 0.001, etc., this means dividing the number by 10, 100, 1000, etc., i.e. it is necessary to move the comma to the left in the decimal fraction by as many digits as there are zeros in front of 1 in the multiplier.

Using the resulting rule, we find the values ​​of the products:

13.45 times 0.01

there are 2 zeros in front of the number 1, so we move the comma to the left by 2 digits, we get 0.1345.

0.02 times 0.001

there are 3 zeros in front of the number 1, which means we move the comma three digits to the left, we get 0.00002.

Thus, in this lesson you learned how to multiply decimal fractions. To do this, you just need to perform multiplication, ignoring the commas, and in the resulting product, separate as many digits on the right with a comma as there are after the comma in both factors together. In addition, we got acquainted with the rule for multiplying a decimal fraction by 0.1, 0.01, etc., and also considered the properties of multiplying decimal fractions.

List of used literature:

1. Mathematics grade 5. Vilenkin N.Ya., Zhokhov V.I. et al. 31st ed., erased. - M: 2013.
2. Didactic materials in mathematics grade 5. Author - Popov M.A. - year 2013
3. We calculate without errors. Works with self-test in mathematics 5-6 grades. Author - Minaeva S.S. - year 2014
4. Didactic materials in mathematics grade 5. Authors: Dorofeev G.V., Kuznetsova L.V. - 2010
5. Control and independent work in mathematics grade 5. Authors - Popov M.A. - year 2012
6. Maths. Grade 5: textbook. for general education students. institutions / I. I. Zubareva, A. G. Mordkovich. - 9th ed., Erased. - M .: Mnemosina, 2009

Like ordinary numbers.

2. We count the number of decimal places in the 1st decimal fraction and in the 2nd. We add up their number.

3. In the final result, count from right to left as many digits as you get in the paragraph above, and put a comma.

Decimal multiplication rules.

1. Multiply without paying attention to the comma.

2. In the product, separate after the comma as many digits as there are after the commas in both factors together.

Multiplying a decimal fraction by a natural number, you need:

1. Multiply numbers, ignoring the comma;

2. As a result, we put the comma so that to the right of it there are as many digits as in the decimal fraction.

Multiplication of decimal fractions by a column.

Let's take an example:

We write decimal fractions in a column and multiply them as natural numbers, ignoring the commas. Those. We regard 3.11 as 311, and 0.01 as 1.

The result is 311. Next, we count the number of decimal places for both fractions. In the 1st decimal fraction there are 2 digits and in the 2nd - 2. Total number digits after commas:

2 + 2 = 4

We count from right to left four characters in the result. In the final result, there are fewer numbers than you need to separate with a comma. In this case, it is necessary to add the missing number of zeros to the left.

In our case, the 1st digit is missing, so we add 1 zero to the left.

Note:

Multiplying any decimal fraction by 10, 100, 1000, and so on, the decimal point is moved to the right by as many digits as there are zeros after one.

For example:

70,1 . 10 = 701

0,023 . 100 = 2,3

5,6 . 1 000 = 5 600

Note:

To multiply a decimal by 0.1; 0.01; 0.001; and so on, you need to move the comma to the left in this fraction by as many digits as there are zeros in front of the unit.

We count zero integers!

For example:

12 . 0,1 = 1,2

0,05 . 0,1 = 0,005

1,256 . 0,01 = 0,012 56