decimal, Yesreal numberA special form of expression of.AllfractionCan be expressed as decimal, and the dot in decimal is calleddecimal point, which is a decimalintegerDividing number of part and decimal part.The integer part isFatal FrameThe decimal of is called pure decimal, and the decimal with integral part not zero is called with decimal.
Add or remove any zero at the end of the decimal part, and the size of the decimal will not change.For example: 0.4=0.400, 0.060=0.06.
Move the decimal point to the right (or left) by n places respectively, and the decimal value will expand (or reduce) the base's nPowerTimes.(For example, for decimal system
）。[1]
classification
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terminating decimal
Limited number after decimal partdigitDecimal of.For example, 3.1465, 0.364, 8.3218798456, etc., finite decimals belong toRational number, which can be converted into fractional form.
From a certain place in the decimal part, a number or several numbers that repeatedly appear in turn are called cyclic decimals.For example, 1/7=0.142857142857142857142857, 11/6=1.833333, etc.Circular decimals also belong to rational numbers and can be reduced to fractions.
The decimal part has an infinite number of digits, and the decimal of one digit or several digits that do not appear repeatedly in turn is called an infinite non cyclic decimal, such asPiπ=3.14159265358979323……，Natural logarithmOfbase numbere=2.71828182845904……。Infinite non recurring decimal, that isIrrational number, cannot be converted into fraction form.
Conversion of decimals to fractions
Limited decimal fraction: reduced to a fraction of ten (a few percent...).
Pure recurring decimalConversion fraction: the circular node is the numerator. If there is a digit in the circular node, the denominator is 9;The circular node has two digits, and the denominator is 99;The circular node has three digits, and the denominator is 999, and so on.as
，
，
, offer points that can be reduced.
Mixed circular decimalFraction reduction: reduction after the sum of finite decimals and pure cyclic decimals, such as
Some occasions, such asTrading marketOn, generally captured todecimal pointThe last two (whatever is usedRules for rounding off values）, from which other decimal representations are derived.withthree point one four(or3,14）For example:
Before the introduction of the western decimal point in China, there was a set of decimal units in Chinese to represent decimals: minute, centimeter, millionth, silk, hulk, micro, fiber, etc. Each unit was one tenth of the previous one.For example, 3.1416 is read as "three and one quarter and one millionth six silk" or "three and one quarter and one millionth six silk".After the decimal point was introduced into China from the West, the decimal unit was divided and translatedDecimal prefixIt has been gradually used outside, and the current cents and cents will still be used forinterest rate。[2]
