The first unit number and algebra
(A) the understanding of quantity
Positive integer, 0, negative integer
1. There is no object, which is represented by 0. 0 and 1, 2, 3 ... are natural numbers. Natural numbers are integers.
2. The smallest number is 1 and the smallest natural number is 0.
3. 4 degrees Celsius above zero is recorded as +4 degrees Celsius; MINUS 4 degrees Celsius was recorded as MINUS 4 degrees Celsius. "+4" is pronounced +4. "-4" is pronounced as negative four. +4 can also be written as 4.
4. Like +4, 19 and +8844 are all positive numbers. Numbers like -4,-1 1, -7,-155 are all negative numbers.
5.0 neither positive nor negative. Positive numbers are all greater than 0, and negative numbers are all less than 0.
Infinite decimal
1. Fractions with denominators of 10, 100, 1000 ... can be expressed in decimals. One decimal place indicates a few tenths, two decimal places indicate a few percent, and three decimal places indicate a few thousandths. ...
2. Integers and decimals are numbers written in decimal notation, and digits, decimals, hundredths, decimals and percentiles are counting units. The propulsion rate between every two adjacent counting units is 10.
3. The position occupied by each counting unit is called digit. These figures are arranged in a certain order.
4. Properties of decimals: Add "0" or remove "0" at the end of decimals, and the size of decimals remains unchanged.
According to the nature of decimals, we can usually remove the "0" at the end of decimals and simplify decimals.
6. The general method of comparing decimal sizes: first, compare the numbers of integer parts, and then compare the numbers of decimals, percentiles and thousandths in turn from left to right. If the number in any number is large, the decimal number is also large.
7. To rewrite a number into a number with the unit of "10,000" or "100 million", just add a decimal point to the right end of 10,000 or 100 million digits, and then add the words "10,000" or "100 million" after the number.
8. General method for finding decimal divisor:
(1) First, specify how many decimal places to keep;
(2) according to the need to determine which number to see;
(3) Use the method of "rounding" to get the result.
9. Numerical sequence table of integers and decimals: integer part, decimal part … billion digits … billion digits; Millions of digits; Ten decimal places; Ten decimals … Counting unit … Billion Billion Billion Billion Billion … True fraction, False fraction.
1. Divide the unit "1" into several parts on average, and the number representing such one or several parts is called a fraction. The number representing one of them is the decimal unit of this fraction.
When two numbers are divided, their quotient can be expressed by fraction. Namely: a÷b=(b≠0)
3. As can be seen from the meaning of decimal and fraction, decimal is actually a fraction with denominators of 10, 100 and 1000. ...
4. Scores can be divided into true scores and false scores.
Fractions with numerator less than denominator are called true fractions. The true score is less than 1.
6. Fractions with numerator greater than or equal to denominator are called false fractions. False score is greater than or equal to 1.
7. The fraction whose numerator and denominator are only the common factor 1 is called simplest fraction.
8. The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number at the same time (except zero), and the size of the fraction remains unchanged.
9. The nature of decimals is consistent with the basic nature of fractions. Using the basic properties of fractions, we can divide and divide.
Percentage tax rate, interest, discount, percentage
1. A number indicating that one number is a percentage of another number is called a percentage. Percentage is also called percentage or
Percentage, which is usually expressed as "%".
2. Comparison of scores and percentages: The same scores with different points can represent specific quantities, and there can be unit names to represent the relationship between two numbers. Percentages cannot represent specific quantities, nor can they have company names. 3. Integration of fractions, decimals and percentages.
(1) Decimalize the fraction and divide it by the denominator.
(2) Take the number of components in decimal, first rewrite the scores with components of 10, 100, 1000 ... and then lower the scores.
(3) Turn the decimal point into a percentage, first move the decimal point to the right by two places, and then add hundreds of semicolons.
(4) To change the percentage into a decimal, first remove the percent sign, and then move the decimal to the left by two places.
(5) Turn the fraction into a percentage, first turn the fraction into a decimal (three decimal places are generally reserved when it is used up), and then turn the decimal into a percentage.
(6) First rewrite the percentage number of components into the number of components, and the quotation that can be reduced becomes the simplest score.
4. Mutual exchange of three commonly used numbers in memory. =0.5=50% ≈0.333=33.3% ≈0.667=66.7% =0.25=25% =0.75=75% =0.2=20% =0.4=40% =0.6=60% =0.8=80% ≈0. 167= 16.7% ≈0.833=83.3% =0. 125= / kloc-0/2 .5% =0.375=37.5% =0.625=62.5% =0.875=87.5% =0. 1= 10% =0.3=30% =0.7=70% =0.9=90% =0.05=5% =0. 15= 1 5% =0.35=35% =0.45=45% =0.55=55% = 0.65 = 65% = 0.85 = 85% = 0.95 = 95% = 0.04 = 4% = 0.025 = 2.5% = 0.02 = 2% = 0.0 1 = 1% 5.
The percent of pass indicates the percentage of qualified parts in the total number of parts.
Survival rate refers to the percentage of surviving trees in the total number of trees.
6. To find the percentage of one number greater than another is to find the percentage of one number greater than another.
7. More "1"= a few percentage points more "1"= a few percentage points less.