1. Define decimals
Decimal refers to a number with finite or infinite digits after the decimal point. For example, 0.5, 1.234, etc.
2. The essence of decimal system
Decimals can be expressed by fractions. For example, 0.5 can be written as 1/2. Decimals are related to size, so you can use the size symbol (
3. Classification of decimals
According to the number of digits after the decimal point, it can be divided into finite decimal and infinite decimal. According to the cycle of digits after decimal point, it can be divided into cyclic decimal and acyclic decimal. According to whether the integer part before decimal is 0, it is divided into pure decimal and decimal with integer part.
4. Decimal conversion
Decimals can be converted into fractions, and the digits after the decimal point are numerator and denominator. Fractions can also be converted into decimals and directly divided.
5. Decimal operation
Addition and subtraction: bit-aligned, add 0 before and after the decimal point, and then add and subtract according to the integer.
Multiplication: Convert decimals into fractions, and then multiply the fractions for operation.
Division: Multiply the dividend and divisor by several times of 10, convert the decimal into an integer, and then divide the integer.
6. Application of decimals
Decimals are common in life, such as weight, temperature, currency, etc. Mathematically, decimals can be used to calculate areas, volumes, etc.
7. Integer and decimal operations
Decimals can also be operated with integers, and the operation is directly carried out according to the decimal algorithm when adding, subtracting, multiplying and dividing; In division, integers should be converted into decimals before operation.
8. Decimal carry and abdication
In decimal calculation, carry and abdication are also needed. Carry refers to adding 1 or binding 1 to the previous digit when one digit after the decimal point is greater than or equal to 5. Abdication means that when one digit after the decimal point is less than 5, the previous digit should be kept unchanged.
9. Decimal truncation method
According to the rounding method of n+ 1 digit after the decimal point, n digits after the decimal point can be retained. If the number n+ 1 after the decimal point is less than 5, it is discarded; On the other hand, enter a.
10. Application example of decimal system
Calculate the area, perimeter and volume of a circle. Calculate the currency exchange of different countries according to the currency exchange rate. Calculate vital data, such as body mass index (BMI).
The above is a mind map of the initial understanding of decimals. By studying and understanding the definition, nature, classification, transformation, operation and application of decimals, we can better master and use decimals.