Rules for dividing into a column of decimal fractions: examples for training

If you do not understand the topic “Division of decimal fractions”, then read the article. There are rules and examples in it.

"Division of decimal fractions" - This is a difficult topic in mathematics. Let's analyze it together and consider how to correctly divide the fraction into a fraction or fraction into other numbers. Read further.

Division of decimal fractions: basics, rules, examples for training

Decimal fractions have a number of numbers that are divided on 10. it 10, 100, 1000 And the same amounts.

Rule: The division process is similar to actions with conventional fractions. Just rewrite the fraction into a primitive look. To divide decimal fractions, first replace them with ordinary ones, and then make calculations.

Here are examples for training:

It happens that in the example of division, certain decimal fractions of a non -periodic property appear. Then the tactics are radically changing. As a rule, they cannot be brought to a “familiar” species.

Therefore, it is necessary to resort to logical rounding. These are the basics of fraction of fractions. Drilling to a certain discharge is carried out. The action can be applied both in relation to the divider and in relation to the divided. This is clearly seen in the example above.

You need to round the final fraction, for accuracy and convenience. But, in fact, in operations with fractions of this species there is nothing extraordinary or difficult - everything is simple.

How to divide a natural number into decimal fraction and vice versa?

The scheme is quite simple: first, we replace the periodic and final fractions simple, and then we round the non -periodic ones. Understanding the principle is very simple with examples:

How to divide decimal fraction into natural number: rule, examples

Now let's see how to divide the decimal fraction into a natural number. Here's a rule and an explanation of actions:

• The solution is made according to the rules of the “standard” division into a column. At first, you can not pay attention to a comma. However, one cannot forget about her.
• The comma is placed in the private at the stage when the process of dividing the whole part of the divisible is completely completed.
• If the whole part of the divisible as a result of the inspection is slightly less than the present divisor, then in the private it is worth putting “0 whole”.

This definition is clearly visible on examples:

Many people think that the division of the column helps out only in mathematical operations with established natural numbers. In fact, in the case of fractions, this simple way is also applicable. To divide decimal fractions into natural numbers with a column, you need:

• Add to the decimal fraction of zeros.
• Divide decimal fraction into a natural number (column). When the process is completed, put in a private comma and continue calculations.
• The result will certainly be a fraction (final or endless), depending on the current residue. The final result will be in the case of zeros. And if the remains are repeated, then we will get a periodic fraction.

As you can see, the remnants are repeated, the numbers are also alternated in the private. Therefore, it is worth writing down the answer: $6,0(925).$

How to divide one decimal fraction into another: a column, multiplication

To facilitate the process, we are sure to multiply divisible and divider by the number with zero: 10, 100, 1000 and numbers with a large number of zeros. Thus, the divider automatically turns into a natural number. Then the actions, of course, are repeated. Everything is due to the properties of division and multiplication.

It's important to know:It is necessary to focus on the final number of signs located after aim. The first fraction is analyzed. Suppose 6,33 has become a whole, it multiplies by one hundred: (6, 33 · 100): (0.3 · 100) . And then at 100 each of the decimal fractions is multiplied \u003d 633: 30.

Then the usual numbers are simply divided - methodically and in a column. But remember that the decimal fractions were originally shared. Divide decimal fraction 0.1, 0.01, 0.001 - The same as multiply her 10, 100, 1000 respectively.

To divide the final decimal shot to another, it follows:

• To resort to the transfer of a comma in divisible and divisor to the right number of signs, which will turn the divider into a natural number. If the signs in divisible are not enough for some reason, then the necessary zeros are added on the right side.
• Next, we just divide the fraction into the column by the number that turned out. As you can see, the scheme is very logical and elementary.

Here are examples of solutions by a column:

By this method, a natural number can be divided into decimal fraction. Here is an example of how it is done:

Divide decimal fractions by 1000, 100, 10: how to do it right?

Based on the existing and well -known rules for dividing the so -called “ordinary fractions”, division into numbers with zeros is equivalent to multiplication. It is necessary to transfer the comma to the right number of digits. If there are not enough values, zeros are simply added. The same happens with endless decimal fractions.

Therefore, in order to correctly perform the division of a decimal fraction into numbers with zeros, you need to transfer the comma to as many numbers as zeros after a unit in a divider: if it is number 10 - That is zero alone, if 100 - Two. And so on.

Examples with endless fractions are also decided by:

Division of decimal fractions by 0.001, 0.01, 0.1: how to do it correctly?

Decimal fractions division technique 0.001, 0.01, 0.1 Similar:

• Fractions are divided into these values \u200b\u200bsimilarly to multiplication 1000, 100, 10.

As a rule, depending on the existing conditions, the comma is transferred to 1-3 digits. If the numbers are not enough, then how to do it correctly?

• A few more zeros are added.

Example:

A similar method is used in the case of decimal fractions of an infinite property. The main thing is to pay attention to the resulting period. Otherwise, inaccuracy may occur in calculations.

How to divide a mixed number or ordinary fraction into decimal and vice versa?

Another example of division in mathematics is the division of a mixed number or ordinary fraction into decimal and vice versa. How to do it right? Here's the rule:

• Everything comes down to banal procedures with ordinary fractions.
• The decimal numbers by analogy are replaced by fractional, and the mixed number is written in the form of a wrong fraction.

If non -periodic fraction is divided into ordinary, or by the number mixed, then the order is reverse:

• Ordinary fraction will be replaced by the appropriate decimal.

Such manipulations allows you to make calculations quickly and simply, not confused in numbers and signs.

Video: Mathematics 5 Division of a decimal fraction by a natural number

Read on the topic:

• Mathematical riddles for children: interesting
• Poems about numbers
• Mathematical rebels for a finete of grade 1-7
• The name of the teams and motto in KVN at the school in mathematics
• Learning to write numbers with a child from 1 to 10