How to read integers: read the names of all levels (hundreds of millions, tens of thousands) from the previous level, and don't read the zeros at the end of each level. One or several zeros in other numbers only read a "zero".
Integer writing: write from the high position, and write 0 if there is no unit.
Rounding method: Find the divisor according to the digit with the highest mantissa. If it is less than 5, it is rounded, equal to or greater than 5. Rounds the mantissa forward by 1. This method of finding the divisor is called rounding.
Integer size comparison: the number with more digits is larger, the number with the same digit is larger, the number with the same digit is larger than the number with the second digit, and so on.
Decimal part:
Divide the integer 1 into 10, 100, 1000 ... These fractions are tenths, hundredths, thousandths ... These fractions can be expressed in decimals. For example,110 is recorded as 0.
The first digit to the right of the decimal point is called the tenth digit, and the counting unit is one tenth (0.1); The second number is called the percentile, and the counting unit is one hundredth (0.0 1) ... The maximum counting unit of the decimal part is one tenth, and there is no minimum counting unit. There are several figures in the decimal part, which are called decimals. For example, 0.36 is two decimal places and 3.066 is three decimal places.
Decimal reading: integer reading, decimal reading, sequential decimal reading.
Decimal writing: the decimal point is written in the lower right corner of the unit.
The essence of decimals: add 0 at the end of decimals and keep 0 unchanged. Simplify.
Decimal position shift causes size change: shift to the right expands and decreases to the left,1.1230,000 times.
Decimal size comparison: if the integer part is big, it will be big; If the integers are the same, ten digits will be big; And so on.
Fractions and percentages
■ The meaning of fractions and percentages
1, the meaning of the fraction: divide the unit "1" into several parts, and the number representing such one or several parts is called the fraction. In a fraction, the number representing how many parts the unit "1" is divided into is called the denominator of the fraction; A number indicates how many copies have been made, which is called the numerator of the fraction; One of them is called fractional unit.
2. The meaning of percentage: The number indicating that one number is the percentage of another number is called percentage. Also called percentage or percentage. Percentages are usually not written in the form of fractions, but are expressed by a specific "%". Generally, percentage only indicates the multiple relationship between two quantitative relationships, and it cannot be followed by the company name.
3. Percent indicates the ratio relationship between two quantities, and the unit of measurement cannot be written behind it.
4. Percentage: A few percent is a few tenths.
■ Fraction type
According to the different conditions of numerator, denominator and integer, it can be divided into true fraction, false fraction and band fraction.
■ The relationship between fraction and division and the basic properties of fraction.
1, division is an operation with operation sign; The score is a number. Therefore, it should generally be said that dividends are equivalent to a molecule, but it cannot be said that dividends are a molecule.
2. Because there is a close relationship between fraction and division, the basic properties of fraction can be obtained according to the "quotient invariance" property in division.
3. The numerator and denominator of a fraction are multiplied or divided by the same number (except 0), and the size of the fraction remains unchanged. This is called the basic nature of fraction, which is the basis of divisor and total fraction.
■ Simplified points and general points
1, the fraction whose numerator and denominator are prime numbers is called simplest fraction.
2. Making a fraction equal to it but with smaller numerator and denominator is called reduction.
3. Reduction method: divide the denominator by the common divisor of the denominator (except 1); Usually, we have to divide until we can get the simplest score.
4. Dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called the total score.
5. General division method: first find the least common multiple of the original denominator, and then turn each fraction into a fraction with this least common multiple as the denominator.
■ Reciprocity
Two numbers whose product is 1 are reciprocal.
To find the reciprocal of a number (except 0), just switch the numerator and denominator of this number.
3. The reciprocal of 1 is1,and 0 has no reciprocal.
■ Score comparison
1, the fraction with the same denominator, the larger the numerator, the greater the fraction.
2. The scores with the same numerator are larger with smaller denominator.
3. Fractions with different denominators and numerators are usually divided into fractions with a common denominator and then compared.
4. If you score the compared scores, first compare their integer parts, and the score with the larger integer part is larger; If the integer parts are the same, compare their decimal parts, and the decimal part with the largest decimal part is the largest.
■ Correlation among percentage, folding and percentage:
For example, a 70% discount is 30%, a 75% discount is 75%, and the percentage is several ten thousandths. For example, a discount of 10% means poor quality. 0%, 65% is 65%.
■ Taxes and interest:
Tax rate: the ratio of taxable amount to various incomes.
Interest rate: the percentage of interest and principal. Calculated by the bank on an annual or monthly basis.
Calculation formula of interest: interest = principal × interest rate × time.
There are three main differences between percentages and fractions:
1. The meaning is different. Percent is "a number indicating that one number is a percentage of another." It can only express the multiple relationship between two numbers, but not a specific number. For example, it can be said that 1 meter is 20% of 5 meters, and it cannot be said that "a rope is 20% meters long." Therefore, the percentage cannot be followed by the company name.