Integers include natural numbers and negative integers, or integers consist of positive integers, zero integers and negative integers. (1) natural number

Meaning of natural numbers: When we count objects, the numbers 0, 1, 2, 3, 4, 5, ... are called natural numbers. The number of natural numbers is infinite and there is no maximum natural number.

Meaning of "0": "0" means that there is no object, and it occupies a place in counting, which means that there is no counting unit on this number. "0" can also indicate the starting point, demarcation point, etc. "0" is the smallest natural number. (2) Positive numbers

Definition of positive numbers. Numbers like 8,16,200 ...................................................................................................................................................

The writing and reading of positive numbers can also be preceded by a+sign, for example, +8 is pronounced as: plus eight. You can usually omit the "+"sign. (3) Negative numbers

Definition of negative numbers Numbers like-1, -5,-132 are called negative numbers. "One" is called negative sign. The writing and reading of negative numbers begin with "one", for example,-15 is pronounced as: negative fifteen. The larger the number, the smaller the negative number.

"0" is neither positive nor negative. (4) The connection and difference between integer and natural number.

Natural numbers are all integers, and integers are not all natural numbers, including negative integers. Knowledge point 2: percentage 1, the meaning of percentage.

(1) A fraction with a denominator of 100 is called a percentage.

(2) A number indicating that one number is a percentage of another number is called a percentage. Percentage is also called percentage or percentage.

Percent application problem knowledge points induction:

1, and find the common percentage, such as: compliance rate, pass rate, survival rate, germination rate, attendance rate, etc. To find a percentage is to find the percentage of one number to another.

2. Find out how much one number is more (or less) than another. In real life, people often use a few percent increase, a few percent decrease and a few percent deposit to express the range of increase or decrease.

How many percentage points more than B (A-B) and how many percentage points less than A (A-B).

3. Find the percentage of a number (unit "1") × percentage.

4. What percentage of a number is known? Find the percentage of this number = a number (unit "1").

A few discounts are only a few tenths, that is, tens of percent. 6. Money deposited in the bank at a certain interest rate is called principal. The extra money paid by the bank when withdrawing money is called interest. The ratio of interest to principal is called interest rate. Interest = principal × interest rate× time

Percentages are usually not expressed in the form of fractions, but by the symbol "%",which is called the percent sign.

Knowledge point 2: Decimal 1, the meaning of decimal

Divide the integer "1" into 10, 100, 1000 ... such 1 is a few tenths, a few percent, and a few thousandths ... which can be expressed in decimals. One decimal place indicates a few tenths, two decimals indicate a few percent, and three decimals indicate a few thousandths. Comparison of decimal sizes in ............

Comparing the sizes of two decimals, first look at their integer parts, and the number with the larger integer part will be larger; The same is true for the integer part, where is the largest number in the tenth digit; Decimals are the same, and the number with the largest number in the percentile is larger ... 3. Rewrite the number and find the divisor.

Rewriting and omitting numbers A method of writing the mantissa after a certain number of this number into a divisor.

For the convenience of reading and writing, large numbers are often abbreviated to "10,000" or "100 million". For example: 2365500 = 2365500 (rewrite the number as "ten thousand"). Sometimes you can omit the mantissa of this number and write it as an approximation as needed. For example, 2,365,500 ≈ 2.37 million (the mantissa after ten thousand digits is omitted), sometimes it is required to keep a decimal approximation. Such as: 7.62983≈7.6 (keep one decimal place).

When taking divisors, methods such as rounding, one-step method and one-step method are often used to omit the mantissa after a certain digit of a number.

Knowledge point 3: score

1, the meaning unit of a fraction "1" is divided into several parts on average, and the number representing such one or several parts is called a fraction.

2. Decimal unit "1" This unit is divided into several parts on average, indicating a part of the score, which is called decimal unit.

3. Classification of scores

(1) Fractions with numerator less than denominator are called true fractions.

(2) Fractions with numerator greater than or equal to denominator are called false fractions.

4, the basic nature of the score The numerator and denominator of the score are multiplied or divided by the same number (except 0) at the same time, and the size of the score remains unchanged. This is called the basic nature of music score.

5. Relationship between Fraction and Division (1) The numerator of Fraction is equivalent to the dividend of Division, the denominator of Fraction is equivalent to the divisor of Division, and the fractional line is equivalent to the divisor of Division. (2) In division, the divisor in the fraction cannot be 0 and the denominator cannot be 0. Division is meaningless, and the denominator is 0.

6. The process of simplifying a fraction into a fraction that is equal to it and has smaller numerator and denominator is called simplification.

7, simplest fraction numerator, denominator is a prime number fraction called simplest fraction.

8. Comprehensive score refers to the conversion of scores of different denominators into scores of the same denominator equal to the original score, which is called comprehensive score. 9. Comparison of the size of fractions Two fractions with the same denominator, the larger the numerator, the greater the score; For two fractions with the same numerator, the fraction with smaller denominator is larger.

10, Decimal Decimal Decimal According to the relationship between fraction and division, the fraction is converted into a division formula, and then the decimal can be obtained by calculation.

1 1, decimal places have several decimal places, so write a few zeros after 1. 12, the relationship between the basic properties of fractions and the basic properties of decimals

The basic properties of fractions are consistent with those of decimals. Add "0" after the decimal point.

Or removing "0" is equivalent to expanding (or reducing) the numerator and denominator of the corresponding score to the original 10 times (or), 100 times (or), 1000 times (or).