Counting units and numerical counting units, numerical and decimal counting methods.
Rewrite Numbers (Omit)
1. Rewrite multiple numbers into "10,000" and "100 million"
Direct rewriting: first move the decimal point of the original number to the left by 4 or 8 places (the decimal part should be crossed out at the end of 0), then add 10000 or 10000 million, and add "=" in the middle.
Omitted mantissa is rewritten as a divisor: the mantissa after 10,000 digits or 100 million digits is omitted by rounding, and then 10,000 digits or 100 million digits are added after the number to obtain a divisor, and the middle is connected by "√".
2. Find the decimal approximation. According to the requirements, wherever decimal places are reserved, the mantissa after this digit should be omitted by rounding, such as 1.5 ≈ 2, 1.4 ≈ 1. Use ""in the middle.
3. Reciprocity between false fraction and band fraction or integer. (from the network)
1. Turn a false fraction into a fraction: the denominator is unchanged, the integer obtained by dividing the numerator by the denominator is the integer part with the fraction on the left, and the remainder is the numerator.
2. Turn the band fraction into a false fraction: the denominator is unchanged, and the numerator is the product of the sum of the integer part and the denominator plus the original molecule. 3. Divide the band into integers: divider ÷ divider = divider/divider, and the divisible band is an integer.
Interoperability among fractions, decimals and percentages. Fractional decimals (from the network), that is, numerator divided by denominator, are decimals, which are converted into percentages, that is, multiplying decimals by 100, and then adding a% sign after them, and vice versa.
For example, 1/4 is converted into a decimal, that is, 1 divided by 4=0.25 is a decimal, and then converted into a percentage, that is, 0.25* 100=25 plus%, which is 25%. If 25% is converted into a decimal, that is, the percentage sign is removed, now it is divided by 100 25/65438+.
Number comparison, integer size comparison, decimal size comparison, decimal size comparison
The nature of numbers, the basic nature of fractions, the basic nature of decimals, and the changing law of decimal size caused by decimal position movement.
Cognitive factor, multiple, odd (jο) number, even number, prime number (prime number), composite number, factorization prime factor, greatest common factor of numbers, least common multiple.
The meaning of four operations and counting methods: addition meaning, subtraction meaning, multiplication meaning, division meaning, addition, subtraction, division, multiplication and checking.
Algorithms and simple methods, elementary arithmetic.
Additive commutative law, additive associative law, multiplicative commutative law, multiplicative associative law, multiplicative distributive law, properties of continuous reduction, properties of quotient invariance.
Subtraction property: a-(b+c) = a-b-ca-(b-c) = a-b+c.
Classification of operations: addition and subtraction are called first-order operations; Multiplication and division are called two-stage operations (abbreviated)
Compound application formula and equation equation measurement unit
Series Properties among Length, Area, Volume and Their Similarities
The unit of measurement and the forward speed between them are 1 ton = 1000 kg = 1000 g.
Time unit exchange rate
Ratio and proportion
Positive proportion, inverse proportion, simplified proportion, ratio, ratio and fraction, division, ratio, proportion, solving application problems with proportion
Graphics and space
Graph, space, perimeter, area, lateral area, surface area, graph transformation, graph and position, graph understanding and measurement.
Statistics and possibilities
Statistical table, statistical chart, average, median, mode, possibility
(1) integer
Meaning of integer 1: … Numbers like -4, -3, -2,-1, 0, 1, 2, 3, … are called integers.
2 natural numbers: when we count objects, 1, 2, 3 ... the numbers used to represent the number of objects are called natural numbers. There is no object, which is represented by 0.
Counting units one (one), ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million, one hundred million ... are all counting units. The propulsion rate between every two adjacent counting units is 10. This counting method is called decimal counting method.
4-digit counting units are arranged in a certain order, and their positions are called digits.
Divisibility of the number 5: The integer A is divisible by the integer B (b≠0), and the divisible quotient is an integer without remainder, so we say that A is divisible by B, or that B is divisible by A. If the number A can be divisible by the number B (b≠0), then A is called a multiple of B, and B is called a divisor (or factor) of A.. Multiplication and divisor are interdependent. Because 35 is divisible by 7, 35 is a multiple of 7, and 7 is a divisor of 35. 7. What is the ratio? The division of two numbers is called the ratio of two numbers. For example, the ratio of 2÷5 or 3:6 or 1/3 is multiplied or divided by the same number at the same time, and the ratio remains unchanged.
8. What is proportion? Two formulas with equal ratios are called proportions. For example, 3:6=9: 18
9. Basic properties of proportion: In proportion, the product of two external terms is equal to the product of two internal terms.
10, solution ratio: the unknown term in the ratio is called the solution ratio. Such as 3:χ=9: 18.
Solution ratio is based on the basic nature of proportion.
1 1, ratio: two related quantities, one changes and the other changes. If the corresponding ratio (i.e. quotient k) of these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. For example: y/x=k(k must be) or kx = y.
12, inverse ratio: two related quantities, one changes and the other changes. If the product of two corresponding numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. For example: x×y=k(k must be) or k/x = y.
Percentage: a number that indicates that one number is a percentage of another number, which is called percentage. Percentages are also called percentages or percentages. 13. To convert decimals into percentages, just move the decimal point to the right by two places and add hundreds of semicolons. In fact, to convert a decimal into a percentage, just multiply this decimal by 100%. To convert percentages to decimals, simply remove the percent sign and move the decimal point two places to the left.
14. When a fraction is converted into a percentage, it is generally converted into a decimal (except for the inexhaustible, three decimal places are generally reserved), and then the decimal is converted into a percentage. In fact, to turn a fraction into a percentage, you must first turn the fraction into a decimal and then multiply it by 100%. Divide the percentage into components, and rewrite the percentage into components first, so that the quotation that can be lowered can be made into the simplest score.
15, we need to learn how to decimal the number of components and how to decimal fractions.
16, greatest common factor: several numbers can be divisible by the same number at the same time, and this number is called the greatest common factor of these numbers. (or the common divisor of several numbers is called the common divisor of these numbers. The largest one is called the greatest common divisor. ) 17, prime number: Two numbers whose common factor is only 1 are called prime numbers.
18, least common multiple: the multiple shared by several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers.
19. Comprehensive score: dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called comprehensive score. (Common divisor is the least common multiple)
20. Approximation: It is called approximation to change a fraction into a fraction equal to it, but with smaller numerator and denominator. (Use the greatest common factor in approximation points)
2 1, simplest fraction: The fraction whose numerator and denominator are prime numbers is called simplest fraction. At the end of the score calculation, the score must be converted into the simplest score. Numbers with units of 0, 2, 4, 6 and 8 can all be rounded to 2, that is, 2 can be subtracted. A number with a bit of 0 or 5 can be divisible by 5, that is, it can be subtracted by 5. Pay attention to the use of contracts.
22. Even and odd numbers: Numbers divisible by 2 are called even numbers. Numbers that are not divisible by 2 are called odd numbers.
23. Prime number (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number). 24. Composite number: a number. If there are other divisors besides 1 and itself, such numbers are called composite numbers. 1 is neither prime nor composite.
25. Interest = principal × interest rate × time (time is generally in years or months, which should correspond to the unit of interest rate).
26. Interest rate: The ratio of interest to principal is called interest rate. The ratio of interest to principal for one year is called annual interest rate. The ratio of interest to principal in January is called monthly interest rate.
27. Natural number: An integer used to represent the number of objects is called a natural number. 0 is also a natural number.
28. Cyclic decimal: A decimal in which one or more numbers are repeated from a certain position in the decimal part. Such decimals are called cyclic decimals.