How to tell if a fraction can be reduced to a finite decimal

After the fraction is reduced to the simplest fraction, the denominator does not contain prime factors other than 2 and 5, and the fraction can be determined to be a finite decimal, otherwise it cannot be reduced to a finite decimal.

For example: 9 150

After the simplest score, it is 3 50

The denominator decomposition prime factor is 50 = 2 5 5, and there is no prime factor other than , so it can be reduced to a finite decimal.

Denominator 24 = 2 2 2 3

There is a prime factor of 3, so it cannot be reduced to a finite decimal.

In the case of a fraction in the simplest part, if its denominator contains only two prime factors, 2 and 5, the fraction can be reduced to a finite decimal.

For example: 6 25=, the denominator 25 only contains the prime factor 5, so 6 25 can be reduced to a finite decimal.

5 16=, the denominator 16 only contains prime factor 2, so 5 16 can be reduced to a finite decimal.

7 20 = , the denominator 20 only contains prime factors 2 and 5, so 7 20 can be reduced to a finite decimal.

5 14, the denominator 14 contains a prime factor 7 in addition to prime factor 2, so 5 14 cannot be reduced to a finite decimal.

In the case of the simplest fraction, look at the denominator of the fraction.

If the denominator contains only two factors, 2 and 5, the fraction can be reduced to a finite decimal.

If the denominator contains a factor other than , it cannot be reduced to a finite decimal.

For example, 9 25 = denominator only contains a factor of 5, which can be reduced to a finite decimal.

7 12 In addition to 2, there is a prime factor 3 in the denominator, which cannot be reduced to a finite decimal.

A simplest fraction, if the denominator contains no prime factors other than 2 and 5, this fraction must be converted into a 、... denominatorscores. Then such a fraction can be reduced to a finite decimal.

When measuring an object, it is common to get a number that is not an integer. So the ancients invented decimal numbers to supplement integers slowly. Decimals are a special representation of decimal fractions.

Decimals can be basically divided into two categories: finite decimal and infinitesimal decimals, and infinitesimal filial piety is divided into two categories: cyclic decimal and infinite non-cyclic decimals. All fractions can be expressed as decimals, except for infinite non-cyclic decimal numbers (irrational numbers).

First of all, there must be a minimum fraction, we decompose the denominator into prime factors, if the denominator contains only these two prime factors, then it can be reduced into finite decimals, such as the denominator remainder contains 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, etc. Celestial laughs.

Here's how fractions can be turned into finite decimals:

A simplest fraction, if the prime factor of the denominator is only 2 or 5, the fraction can be reduced to a finite decimal; If the prime factor of the denominator contains other prime factors in addition to 2 and 5, the fraction cannot be reduced to a finite decimal.

1. Scores

A fraction originally refers to a part of a whole, or more generally, any part of an equal number. It is expressed as a ratio kernel of an integer a and an integer b, and a fraction indicates that one number is a fraction of another number, or the ratio of an event to all events. The unit "1" is divided into several parts, and the number of such parts or parts is called a fraction.

The numerator is on top and the denominator is on the bottom.

2. Finite decimals

When measuring an object, it is common to get a number that is not an integer. The ancients invented decimals to supplement integers. Decimals are a special representation of decimal fractions.

Decimals can be divided into two categories: finite decimal and infinitesimal decimals, all fractions can be expressed as decimals, and decimals can be expressed as fractions except for infinite non-cyclic decimals.

The dot in the decimal is called the decimal point, which is the dividing line between the integer part of a decimal and the decimal part, the part to the left of the decimal point is the integer part, and the part to the right of the decimal point is the decimal part. A decimal with a fractional part of an integer that is zero is called a pure decimal, while a decimal with a non-zero part of an integer is called a decimal. For example:

is a pure decimal place, or it is a decimal place.

3. How to determine which fractions can be turned into finite decimal places as quickly as possible

1. Check whether this score is the simplest score first, if it is not the simplest score, you must first turn it into the simplest score! Remember: if it's not the simplest score, you can't judge it directly.

2. Decompose the denominator of this simplest fraction into prime factors. If the prime factor of the denominator contains 2 or only 5, or both 2 and 5, then the fraction can be reduced to a finite decimal. If there are other prime factors in the denominator besides 2 and 5, then the fraction must not be reduced to a finite decimal.

A simplest fraction that contains only 2 and 5 prime factors in the denominator and no other prime factors can be reduced to a finite decimal. If the denominator of a simplest fraction contains a factor other than 2 and 5, the fraction cannot be reduced to a finite decimals.

A simplest fraction that cannot be reduced to a finite decimal number must be reduced to an infinite loop of small empty objects. In this case, the denominator of the fraction is broken down into prime factors. If it contains only prime factors other than 2 and 5, and no 2 and 5, it can be converted into a pure cyclic decimal.

For example, 2 3 = If there are both 2 and 5 in the denominator, and prime factors other than 2 and 5, this fraction can be converted into a rebate mixed cycle decimal. For example, 8 15 = If there are more numbers in the denominator than 2 and 5, the fraction can be reduced to an infinite non-cyclic decimal. For example, 13 161 = 0745341614907......

Decimals and fractions can be converted into each other, fractions can be turned into infinite circular decimals or finite decimals or integer decimals may not be converted into fractions, infinite non-cyclic decimal is irrational numbers, and decimals are a special form of real numbers.

All fractions can be expressed as decimals, and the dot in the decimal is called the decimal point, which is the dividing point between the integer part of a decimal and the decimal part. Among them, the decimal part of the integer part is called a zero decimal number, and the decimal part of the rock stuffy hall is not zero is called a decimal with a decimals.

How to determine if a fraction can be reduced to a finite decimal place:

In the case of the simplest fraction, if its denominator contains only two prime factors, 2 and 5, the fraction can be reduced to a finite decimal. Otherwise, it cannot be reduced to a finite decimal.

8 25=, the denominator 25 only contains the prime factor 5, so 8 25 can be reduced to a finite decimal.

7 8=, the denominator 8 only contains the prime factor 2, so 7 8 can be reduced to a finite decimal.

7 50 = , the denominator 50 only contains prime factors 2 and 5, so 7 50 can be reduced to a finite decimal.

5 18, the denominator 18 contains a prime factor 3 in addition to the prime factor 2, so 5 18 can not be reduced to a finite decimal.

Looking at the denominator, if the denominator is 2or4or8or5 after the fraction is reduced to the simplest fraction.

If the denominator does not contain other prime factors in addition to two and five, the fraction can be replaced with a finite decimal, for example, the denominator of 17/20 is equal to 2 2 5, it can create a finite decimal, if the denominator contains prime factors other than two and five, a fraction can not be turned into a finite decimal, for example, the denominator of 7/30 is equal to 2 3 5, he cannot be reduced to a finite decimal.

Analysis of elementary math questions: To judge whether a fraction can be reduced to a finite decimal number, it is necessary to simplify it first and then judge.