Whether infinitely cyclic decimal numbers can be added or subtracted directly

Yes, you need to make it into a fraction first.

Infinite cyclic decimal numbers belong to rational numbers, which can be expressed in the form of fractions, and fractions can be directly added and subtracted, so infinite cyclic decimals can be directly added and subtracted.

For example: 1 3=.

First of all, let's be clear: infinite non-cyclic decimal cannot be converted into fractions, so how do infinite cyclic decimals be converted into fractions? Since the number of decimal places is infinite, it is obviously impossible to write ...... tenths, hundredths, thousandthsof the number. In fact, the difficulty of cyclic decimal fractions lies in the infinite number of decimal places.

So I'll start here and find a way to "cut off" the "big tail" of the infinitely looping decimals. The strategy is to use the method of multiplication to expand the infinite loop decimal by ten, hundred, or thousand......foldMake the enlarged infinite loop decimal exactly the same as the "big tail" of the original infinite loop decimal, and then subtract the two numbers, and the "big tail" will be cut off! Let's look at two examples:

Sum into fractions.

And so on, now that we're talking about infinity, we should be clear that since they're all infinite cyclic decimals, then there's no difference in the number of decimal places they count after the decimal point in the loop section, and it's all said to be infinite.

Think 1: i.e. 99 = 47

Then think 2: i.e. 9 then.

It can be seen that the fractional part of the pure cyclic decimal fraction can be written as a fraction as follows: the minimum number of cyclic nodes of the pure cyclic decimal is a few digits, and the denominator is a number composed of several 9s; A molecule is the number of a cyclic node in a pure cyclic decimal.

Sum into fractions.

Think 1: Use to get:

So, think 2:

Use to get: so,

Common infinite non-cyclic decimal numbers include pi and open inexhaustible, root number 2, root number 3, root number 5, etc. But the two most famous infinite non-cyclic decimal places are pi. An infinite non-cyclic decimal is one in which there are an infinite number of digits after the decimal point, but there is no periodic repetition, or no regular decimal place.

Therefore, mathematically it is also called an infinite non-cyclic decimal number as an irrational number.

There are four common forms of irrational numbers.

1. Infinite non-cyclic decimals, e.g., etc.;

2. Radicals, e.g. 2, 3, ( 5-1) 2, etc.;

3. Functional formula, e.g. LG2, sin1 degree, etc.;

4. Special symbols, such as , e, y.

Transformation and operation of irrational numbersThe transformation of irrational numbers is usually related to rational numbers and the operations of addition, subtraction, multiplication and division. Rational numbers can be converted to irrational numbers, and any rational number divided by an irrational number can be turned into an irrational number, but an irrational number cannot be converted to a rational number.

Commonly used algorithms:

Rational number + rational number = rational number;

Irrational number + rational number = irrational number;

Rational number * irrational number = uncertain;

Rational number * irrational number = uncertain;

Infinite non-cyclic decimal numbers include , e, and some open indefinite numbers, such as: 2, 4, 8th root, etc.

Irrational numbers, also known as infinite non-cyclic decimals, cannot be written as a ratio of two integers. If you write it as a decimal form, there are an infinite number of numbers after the decimal point and it does not circulate. Common irrational numbers include the square root of a non-perfect square number, and e (where the latter two are transcendent numbers), etc.

Infinitesimal Introduction:

Decimals can be divided into two categories: finite decimals and infinitesimal decimals, which in turn are divided into two categories: infinitely cyclic decimal and infinitely non-cyclic decimals.

Infinite loop decimals.

A decimal infinite decimal number that repeats the previous digit or a number begins to appear continuously after the decimal point. As such, the number that is repeated is called a circular verse. The abbreviation for cyclic decimal is to omit all the digits after the first recital stanza and add a small dot above the first and last two digits of the reserved cyclic stanza.

Some decimals, although also infinite, are not cyclical. For example, such decimals are called irrational numbers. Irrational numbers are not like cyclic decimals, where each number is repeated, but also belongs to infinitesimal decimals.

As long as it's an irrational number.

Then it's all infinite non-cyclic decimals.

For example, pi and the base e of natural logarithms

And as long as a is not the square of a rational number.

The root number a is an infinite non-cyclic decimals.

For example, root number 2, root number 3, root number 5, and so on.

What are the infinite non-cyclic decimals Common infinite non-cyclic decimals such as root number 2, root number 3, root number 5, and so on. But the two most famous infinite non-cyclic decimal numbers are pi and the base of the natural logarithm e

Infinite non-repeating decimal (English name: infinite non-repeating decimals) is that there are countless digits after the decimal point, but unlike infinite cyclic decimals, it has no periodic repetition, in other words, there is no regularity, so it is also called infinite in mathematics.

Pi is the base of the natural logarithm e=

Root number 2, root number 3, root number 5

1. Infinite non-cyclic decimalsThe decimal part of a number, where the numbers are arranged irregularly and the number of digits is infinite, is called an infinite non-cyclic decimal number.

2. Infinite cyclic decimalsThe decimal part of a number, where there is a number or several numbers that are repeated in sequence, is called a cyclic decimal. For example: ....

3. Finite decimalsThe digits of the decimal part are finite decimal places, which are called finite decimals. For example, , are finite decimals.

How to decimal fractions:

1. To see how many decimal places it is, add a few 0s as the denominator after 1.

2. Remove the decimal point from the original decimal point and make it a numerator.

3. The offer points that can be contracted.

With fractional decimals:

1. The integer part with fractions remains unchanged.

2. Partially divide the true fraction with fraction into a decimal (numerator divided by denominator).

3. Merge the two parts.

The number after the decimal point is called a cyclic decimal number, and the number of digits of the cyclic decimal is infinite.

In cyclic decimal numbers, the number that repeats after the decimal point is called a cyclic section. For convenience, when we write the circular decimal, we only write the first loop section, and add a dot to the first and last digits of this loop section, which is called the loop point.

Cyclic decimals can be converted into fractions, so cyclic decimals are rational numbers.

The decimal infinite decimal number of the previous one or a section of numbers is repeated in sequence from a certain digit after the decimal point, which is called a cyclic decimal, such as a mixed cyclic decimal), a cyclic decimal), a cyclic decimal), etc.

That is, the number after the decimal point has a number that repeats in turn, such as: vulture=

For example, 1 3 is followed by infinite decimal places, and both are 3s.

Again, 1 7

There are infinite 142857 repetitions, and when a certain number is divided by a certain number, and one or more digits after the decimal point of the quotient are repeated an infinite number of times, it is called an infinite loop decimal.

Dividing inexhaustible decimals. If one is divided by three, it gets. It's an infinite loop of decimals.

The digits after the decimal point are infinite, and the decimal number that repeats from a certain digit is an infinite decimal number. Such as:

1. Infinite non-cyclic decimals

The decimal part of a number, where the numbers are arranged irregularly and the number of digits is infinite, is called an infinite non-cyclic decimal number.

2. Infinite cyclic decimals

The decimal part of a number, where there is a number or several numbers that are repeated in sequence, is called a cyclic decimal. For example: ....

3. Finite decimals

The digits of the decimal part are finite decimal places, which are called finite decimals. For example, , are finite decimals.

Infinite cherry tree loop decimals.

are rational numbers. Cyclic decimals have loop knots (loop points) and can be converted into fractions. And because rational numbers are a set of integers and fractions. So infinitely cyclic decimals are rational numbers.

An integer can also be thought of as a fraction with a denominator of one. The decimal part of a rational number is a finite or infinitely destructive loop. Real numbers that are not rational numbers are called irrational numbers.

That is, the decimal part of an irrational number is an infinite number that is not cyclical.

No, in principle, it is not possible to perform four arithmetic operations for infinitesimal numbers.

, an infinite loop of decimals.

It is also an infinite decimal, so an infinite cyclic decimal cannot be arithmetic.

The four operations refer to the four operations of addition, subtraction, multiplication and division. The four arithmetic is elementary mathematics.

It is also the basis for learning other related knowledge.

Subtraction: The operation of finding another addition in the sum of two known additions and one of them. Multiplication: The operation of finding the product of two numbers.

1) Multiplying a number by an integer is a simple operation to find the sum of several identical additions.

2) Multiplying a number by a decimal place is to find the number of tenths and thousandths of the ......How much.

3) Multiplying a number by a fraction is to find out what fractions of the number are. Division: The operation of knowing the product of two factors and one of the factors, and finding the other factor.

OK! Infinite cyclic decimal numbers can be used to add, subtract, multiply, and divide four operations.

No. Infinite is unknown, and unknown cannot participate in computation.

Infinite loop decimals can be turned into fractions, and naturally four operations can be done.

This gives rise to fractions, where infinitesimal fractions themselves cannot be operated in four ways, but fractions can.

Yes, infinitesimal numbers can be operated in four ways: for example, we are familiar with the root number 2 multiplied by the root number 2 equals 2: the root number 2 plus the root number 2 and so on 2 times the root number 2:

Root number 6 divided by root number 3 equals root number 2: root number 2 multiplied by root number 3 equals root number 6: for example, the area of a garden with a radius of root 2 is 2 丌 = 丌 ten 丌; As for the infinite cyclic decimals, when the carry is not involved, the addition and subtraction are calculated according to the law of vertical digital alignment, and the correctness of the results is easy to see, and the multiplication and division method is more complicated because it involves carrying, but it can still be carried out.

In short, real numbers are closed to the four operations (the divisor is not 0), which is a fundamental arithmetic property of the real number system.