Dividers are fractional divisions of integers, which are divided according to the law of integer division. The decimal point of quotient should be aligned with the decimal point of dividend. If there is a remainder at the end of the dividend, add 0 after the remainder and continue the division.
2. Divider is the calculation rule of fractional division:
Divider is the division of decimals. First, move the decimal point of the divisor to make it an integer. The decimal point of the divisor is shifted to the right by several digits, and the decimal point of the dividend is also shifted to the right by several digits (the digits are not enough, and 0 is added at the end of the dividend), and then the calculation is carried out according to the fractional division in which the divisor is an integer.
Discovery in fractional division;
1, when the divisor is greater than 1, the quotient is less than the dividend. For example, 3.5÷5=0.7.
2. When the divisor is less than 1, the quotient is greater than the dividend. For example, 3.5/0.5 = 7.
Calculation method of fractional division:
Quotient× Divider = Divider (General) ② Divider = Divider
Factor of quotient: according to the number of decimal places to be reserved, decide how many decimal places to divide by quotient, and then reserve a certain number of decimal places according to rounding method to find the divisor of quotient.
For example, if you want to keep one decimal place, you can stop dividing the quotient to the second decimal place; If two decimal places are needed, the quotient should stop at the third decimal place, and so on.
Cyclic decimal problem:
1, the number of digits in the decimal part is a finite decimal, which is called a finite decimal. Such as 0.37, 1.4 135, etc.
2. The number of digits in the decimal part is infinite decimal, which is called infinite decimal. Such as 5.3… 7. 145 145… etc.
3. The decimal part of a number, starting from a certain number, one or several numbers appear repeatedly in turn. This decimal is called a recurring decimal. (For example, 5.3 … 3.12323 … 5.7171…)
4. Circulate the decimal part of the decimal system, that is, the numbers that are repeated in turn, which is called the circulating part of the decimal system. (For example, the cycle node of 5.333… is 3, the cycle node of 4.6767… is 67, and the cycle node of 6.958258 … is 258).
A simple method of writing cyclic decimals;
1, only write a loop segment, and write a dot at the first and last position of this loop segment.
2. For example, if there is only one number cycle, write a point on this number, 5.333 ... write 5.3. If there is a cycle of two decimal places, click on these two numbers, 7.4343… write 7.43. If there is a cycle of three or more decimal places, mark the decimal point at the first and last place respectively. 10.732 … Write 10.732.
Variation law in division:?
1. Quotient invariance: Divider and divisor expand or shrink by the same multiple (except 0) at the same time, and the quotient remains unchanged.
2. The divisor remains the same, the dividend expands, and the quotient expands. The dividend is constant, the divisor decreases and the quotient expands. ?
3. The dividend is constant, the divisor decreases and the quotient expands.