What is the fraction of 0 9 cycle, and what is the fraction of 0 9 cycle?

Nine cycles equals 1. This is actually a limit process. Of course, if you are only a junior high school student and do not understand what the limit is, you can understand it this way: nine cycles is equal to three cycles multiplied by 3, that is, 1 3 times 3, which is equal to 1.

Look at the loop score first.

Let x=.

then 10x= cycle.

Subtract 9x=1

So x=1 9

The corresponding cycle score is 1, or 1 1

In fact, in terms of limits, the cycle is infinitely close to 1

Other infinitely cyclic decimal numbers can be combined into fractions by combining sequences and limits, but the problem of loops is not bothered, and the stipulation is equal to 1

Solving problems starts with solving"Definitions".A lot of questions"Definitions"It's not clear.

The cyclic fraction is 1. The decimal part of a number starts from a certain digit, and the infinite decimal number of one or several numbers repeating in turn is called a cyclic decimal.

Circular decimal will have loop sections.

cycle points) and can be converted into fractions.

The decimal system of the previous digit or section of the number is repeated in sequence, starting from a certain digit after the decimal point.

Infinitesimal decimals, called cyclic decimals, such as mixed cyclic decimals), cyclic decimals), cyclic small hood burn collapse numbers), etc., in which the number of the successive cycles that are repeated out of Duan Senxian is called the circular knot.

The abbreviation for cyclic decimal is to omit all the numbers after the first cyclic stanza and add a dot above the first and last two digits of the first cyclic stanza.

Loop) is: 1, and if it has to be written as a fraction, it is 1/1.

Proof 1: Set loop) x.

Then: 10x=loop) then 9x=10x-x=loop) loop) loop)=9.

So x=1, it is proven.

Proof 2: Let the loop) be an infinitely decreasing proportional series.

Then: cycle) = (n-1) power = nth power) (1 to the nth power.

So when n tends to infinity, the nth power tends to 0, so the cycle) 1.

There are two points of view in the mathematical community on this issue:

1. The cycle is equal to 1.

In fact, this proposition should have been confirmed by the mathematical community. This is illustrated by an illustration:

According to the rule of decimal point addition, the addition of decimal points is actually the addition of their respective decimal places, so it is concluded that firstly, cycle + cycle + cycle = cycle, and then 1 3 + 1 3 + 1 3 = 1, and here 1 3 is equal to cycle. So the two are combined to conclude that:

1=Cycle. Second, it is generally accepted that the cycle is not equal to 1:

Intuitively, the loop must < 1, because the loop is infinitely close to 1, but approaching 1 means that it has not been able to reach 1, since it does not reach 1, it proves that it must be smaller than 1, which is also very much in line with our common sense.

The cyclic decimal is special in that it is equal to 1.

The cyclic fraction is 9 9 = 1.

1. The method of pure cyclic decimal, such as: cyclical) = (ab 99), and finally simplified. Here are some examples:

loop) = 3 9 = 1 3;

loop) = 7 9;

loop) = 81 99 = 9 11;

circulation) = 1 and 206 999.

2. The method of mixing the circulation of decimals, such as: circulation) = (abc a) 990, and finally simplifying. Here are some examples:

loop) = (51 5) 90 = 46 90 = 23 45;

circulation) = (2954 29) 9900 = 13 44;

Cycle) = 1 again (4189 4) 9990 = 1 again 4185 9990 = 1 again 31 74.

1. The step method of fraction reduction.

1) Decompose the numerator and denominator into factors.

2) Find the common factor of the numerator and denominator.

3) Eliminate the non-zero common factor.

2. Multiplication of fractions.

1) The fraction is multiplied by an integer, the denominator remains unchanged, the numerator is multiplied by an integer, and finally the offer fraction that can be reduced.

2) Multiply fractions by fractions, multiply numerators by numerators, multiply denominators by denominators, and finally offer fractions that can be reduced.

Summary. Hello, dear. This problem is a special cyclic decimal.

In general, it is commonly known as ninety-nine to one. Any cyclic decimal can be converted into a decimal. Like what.

One cyclic decimal corresponds to a denominator of 9, a two-digit cyclic decimal corresponds to a denominator of 99, and so on.

What is the fraction of the loop.

Hello, dear. This problem is a special cyclic decimal. In general, it is commonly known as the ninety-nine return to the state slippery one.

Any cyclic decimal can be turned into a decimal number. Like what. One cyclic decimal corresponds to a denominator of 9, two cyclic decimal places corresponds to a branch or 99, and so on.

Dear, relevant information: Cyclic decimal is a special form of decimal in which a number is repeated endlessly in the Minor Numbers section. Turning circular decimals into fractions is one of the most common problems in mathematics, and it allows us to convert infinitely looping numbers into rational number expressions, providing a more concise and easy-to-understand representation.

Kisses, the decimal of the cover Tong cycle is generally indicated by an ellipsis or parentheses to indicate the part of the repetition, such as or. We use the letters a, b, lease and chong c to represent the number of the loop segment, assuming that the length of the loop segment is n. then the cyclic decimal can be expressed as:

x = integer part + non-cyclic part + cyclic decimal part. Among them, the non-cyclic part can be expressed in decimal form, and the cyclic decimal part can be expressed in fractional form.

Actually for such circular decimals.

Remembering and 1 is the same thing.

Then because it's 1 9

Then it's 1, so here it is.

Converted into a fraction is 1 2

Circular decimal is certainly a fraction of the search.

As long as there is a decimal number of the spring limit of the world.

Or infinitely looping decimals.

Then it's all scores.

If this is a loop).

The result is a score of 105 999 = 35 333