如何用科学计数法写数字？

指数是一种数学运算，它表示一个数字与自身相乘的次数。它涉及两个数字，称为底数和幂，幂写为底的上标。它显示基数乘以自身的幂次。参见例子，3 ⁴ = 3 × 3 × 3，这里底数是 3，幂是 4，所以 3 乘以自身 4 次。另一个例子，5 ³ = 5 × 5 × 5，这里底数是 5，幂是 3，所以 5 乘以自身 3 次。

科学计数法

科学记数法对于巧妙地表示非常大或非常小的数字很有用。它用于数字以便以标准形式写数字，也有助于写大数字。在科学记数法中，一个数字写成，

a × 10 ^b

• 其中 a 是一个非零数，介于 1 到 10 之间，即 1 ≤ a < 10 并且也是负数，b 可以是任意数。
• 这里 b+1 显示给定数字的位数。

例如，

1. 5000 用科学计数法写成 5 × 10 ³
2. 科学计数法中的 12500 写为 1.25 × 10 ⁴
3. 科学计数法中的 0.02 写为 2 × 10 ^-2
4. -6700 用科学计数法写成 -6.7 × 10 ³

如何用科学计数法写数字？

回答：

In order to express numbers in scientific notation, lets take a look at the below-given cases,

Case 1 When a positive number is greater than 1mIn such a case put a decimal after the first digit.

Step 1 5000 ⇢ 5.000

Now to balance it multiply it by 10^{(b – 1)} where b is the number of digits in the given number, here the number consists of 4 digits so multiply it by 10³.

Step 2 5.000 × 10³.

Note If the given number is negative just put the negative sign in the result.

Example -5000   —>   -5.000 x 10³

Case 2 When the positive number is a very small number i.e. smaller than 1 but greater than 0.

In such a case multiply the number by 10 until it is less than 1, and count how many times you multiply it.

Step 1 0.0098 ⇢ 9.8 (multiplied number 3 times)

Now the number is multiplied by 10 m times. you have to divide the number by 10 m times, to balance it. So instead of dividing it by 10^m multiply it by 10^-m because both means the same.

Step 2 9.8 x 10^-3 

This is the scientific notation.

Note If the given number is negative just put the negative sign in the result.

示例问题

问题1：将70000转换为科学计数法。

解决方案：

Number of digits is 5

So, 70000 = 7 × 10^-5

问题2：将-0.0000845转换为科学计数法

解决方案：

There are 5 digits to reach the first non zero digit

So, -0.0000845 = -8.45 × 10⁵

问题3：将7346.0431转换为科学计数法。

解决方案：

There are 3 digits for decimal point to reach the first digit

So, 7346.0431 = 7.3460431 × 10³