将小数转换为分数

数字是用来表示物体的数量/尺寸的数值，例如表示人的重量、几何形状的长度、货币价值等。数字可以分为多种类型。其中一些是十进制数，整数，有理数，复数等。

十进制数

可以将数字视为十进制数，因此任何整数部分和小数部分都由小数点分隔。当测量一个人/事物的重量时，总是不可能用实数表示，如 50、55 等。有时它可能大于 50 且小于 51，此时十进制数字可能会起作用。

Example: 0.619, 50.5, etc.

分数

以 a/b 形式表示的数可以称为分数。其中 a、b 是任意数字。分数是以分子除以分母的形式表示的（商）数。有理数，无理数被认为是分数。

Example: 619/1000, etc.

让我们考虑一个十进制值 c，这个十进制 c 可以转换为分数 a/b，这样在求解 a/b 时会得到结果 c。

c = a/b

Where c is a decimal number, a/b is a fraction.

要将十进制数转换为分数，我们需要遵循一系列步骤。

小数到分数转换

为了将十进制数转换为分数，需要遵循某些步骤。让我们看看这些步骤，

第 1 步：首先，将十进制数除以 1。

Example: Decimal number 0.72 

On applying step 1 0.72/1 is obtained.

第 2 步：对于分子中的每个小数点，分子和分母都乘以 10。

在此示例中，小数点后给出了 2 个数字，因此分子和分母都乘以 10 两次。

0.72 × 10 × 10/1 × 10 × 10 = 72/100

第 3 步：对第 2 步形成的分数进行简化，直到无法进一步简化为止。

72/100 

= 36/50 

= 18/25

这些是从小数转换为分数时必须遵循的 3 个步骤。

让我们看一些例子来更清楚地了解它。

示例问题

问题 1：将小数 0.1 转换为分数

解决方案：

Step – 1 Divide decimal with 1

= 0.1/1

Step – 2 As there is only 1 number after point so multiply 10 one time to both numerator and denominator.

= 0.1 × 10/1 × 10 = 1/10

Step – 3 The above generated can’t be simplified further so we consider the above fraction 1/10 as final result.

So fraction of 0.1 = 1/10

问题 2：将小数 6.25 转换为分数

解决方案：

Step – 1 Divide decimal with 1

= 6.25/1

Step – 2 As there are 2 numbers after point so multiply 10 two times with both numerator and denominator.

= 6.25 × 10 × 10/1 × 10 × 10 = 625/100

Step – 3 This 625/100 fraction can be simplified to,

625/100 = 125/20 = 25/4

So fraction of 6.25 = 25/4

问题 3：将小数 6.25 转换为带分数。

解决方案：

When a whole number is present before point in decimal number then separate that whole number from decimal number and follow the 3 steps for conversion.

6.25 = 6 + 0.25

Step – 1 Consider the digits that are after the decimal point i.e., 0.25 and Divide decimal with 1

= 0.25/1

Step – 2 As there are 2 numbers after point so multiply 10 two times with both numerator and denominator.

= 0.25 × 10 × 10/1 × 10 × 10 = 25/100

Step – 3 This 25/100 fraction can be simplified to

25/100 = 5/20 = 1/4

Add the separated digit 6 (done before step-1) to formed fraction.

So fraction of 6.25 = $6\frac{1}{4}$

问题 4：将小数 4.372 转换为带分数。

解决方案：

For conversion into mixed fraction, separate the whole number part before the decimal point from decimal value and follow the above specified 3 steps on numbers after decimal points.

4.372 = 4 + 0.372

Step – 1 Consider the digits that are after the decimal point i.e., 0.372 and Divide decimal with 1

= 0.372/1

Step – 2 As there are 3 numbers after point so multiply 10 three times with both numerator and denominator.

= 0.372 × 10 × 10 × 10/1 × 10 × 10 × 10 = 372/1000

Step – 3 This 372/1000 fraction can be simplified to,

372/1000 = 93/250

Add the separated digit 4 (done before step-1) to formed fraction

So fraction of 4.372 =  $4\frac{93}{250}$

问题 5：将小数 0.33 转换为分数

解决方案：

Step – 1 Divide decimal with 1

= 0.33/1

Step – 2 As there are 2 numbers after point so multiply 10 two times with both numerator and denominator.

= 0.33 × 10 × 10/1 × 10 × 10 = 33/100

Step – 3 This 33/100 fraction can’t be simplified so it can be leaved as it is

So fraction of 0.33 = 33/100 

问题 6：将小数 0.3333... 转换为分数

解决方案：

Step – 1 Divide decimal with 1

= 0.3333…./1

Note: For this kind of recurrence number i.e., 3 is recurring for infinite times we can’t multiply 10 for each decimal point. In this case we multiply numerator and denominator with 3.

Step – 2 As this is a recurrence number we multiply 3 with numerator and denominator.

0.3333…. × 3/1 × 3 = 0.9999…./3

Step – 3 Simply the above fraction.

As 0.9999… is close to 1, round up the numerator to 1.

0.9999…./3 can be simplified to 1/3.

So fraction of 0.3333… = 1/3