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将分数转换为小数的方法是什么？
将分数转换为小数的方法是什么？
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什么类型的小数有无限的数字？
什么类型的小数有无限的数字？
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将小数相加或相减时，需要做什么？
将小数相加或相减时，需要做什么？
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如何比较小数的大小？
如何比较小数的大小？
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小数的乘法需要做什么？
小数的乘法需要做什么？
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Study Notes
Fractions
Definition and Basics
- A fraction is a way to show part of a whole as a ratio of two numbers
- Consists of a numerator (top number) and a denominator (bottom number)
- Numerator tells how many equal parts are being referred to
- Denominator tells how many parts the whole is divided into
Types of Fractions
- Proper fractions: numerator is less than the denominator (e.g. 1/2)
- Improper fractions: numerator is greater than or equal to the denominator (e.g. 3/2)
- Mixed numbers: a combination of a whole number and a proper fraction (e.g. 2 1/2)
Operations with Fractions
- Addition and subtraction: require common denominators
- Multiplication: multiply numerators and denominators separately
- Division: invert the second fraction (i.e. flip the numerator and denominator) and then multiply
Equivalent Fractions
- Fractions that have the same value, but different numerators and denominators
- Can be created by multiplying or dividing both numerator and denominator by the same number
Decimals
Definition and Basics
- A decimal is a way to show part of a whole as a number with a fractional part
- The fractional part is separated from the whole number part by a decimal point
- Each place value to the right of the decimal point represents a power of 10 (e.g. tenths, hundredths, etc.)
Converting Fractions to Decimals
- Divide the numerator by the denominator to convert a fraction to a decimal
- Terminating decimals: have a finite number of digits (e.g. 1/2 = 0.5)
- Repeating decimals: have an infinite number of digits that repeat in a pattern (e.g. 1/3 = 0.333...)
Operations with Decimals
- Addition and subtraction: line up the decimal points and perform the operation
- Multiplication: multiply the numbers as usual, then place the decimal point in the product
- Division: divide the numbers as usual, then place the decimal point in the quotient
Comparing and Ordering Decimals
- Compare decimals by comparing the digits from left to right
- Order decimals from least to greatest or greatest to least by comparing the digits from left to right
分数
定义和基础
- 分数是表示整体的一部分作为两个数字的比率
- 由分子（上数字）和分母（下数字）组成
- 分子表明有多少个相等的部分被参照
- 分母表明整体被分成多少部分
分数类型
- 正确分数：分子小于分母（例如 1/2）
- 不正分数：分子大于或等于分母（例如 3/2）
- 混合数：一个整数和一个正确分数的组合（例如 2 1/2）
分数运算
- 加法和减法：需要相同的分母
- 乘法：分别乘分子和分母
- 除法：将第二个分数倒过来（即交换分子和分母），然后相乘
等价分数
- 具有相同值的分数，但不同的分子和分母
- 可以通过将分子和分母同时乘或除以相同的数字来创建
小数
定义和基础
- 小数是表示整体的一部分作为一个带有小数部分的数字
- 小数部分与整数部分由小数点分隔
- 小数点右侧的每个位值表示 10 的幂（例如十分位、百分位等）
将分数转换为小数
- 除以分母将分数转换为小数
- 终止小数：具有有限位数字（例如 1/2 = 0.5）
- 循环小数：具有无限位数字的重复模式（例如 1/3 = 0.333...）
小数运算
- 加法和减法：对齐小数点然后进行运算
- 乘法：正常相乘，然后将小数点放在积中
- 除法：正常相除，然后将小数点放在商中
比较和排序小数
- 通过从左到右比较数字来比较小数
- 通过从左到右比较数字来排序小数，从小到大或从大到小
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