科学计数法中的加法和减法
科学记数法是一种以简单的表示形式表示大数和小数的方法。任何数字都可以用这种科学记数法表示，使得该数字介于 1（一）和 10（十）之间，并乘以 10 的幂。
Example: 7200000 (72 Lakhs) can be represented in scientific form as 7.2 × 106
Here 7200000 is represented as 7.2 multiplied by 10 to the power of 6.
科学计数法加法
我们可以在以科学计数法表示的两个或多个数字之间进行加法。为了解释以科学计数法执行加法的方法，请考虑一个示例
2 × 10 2 + 3 × 10 2
在解决上述问题之前，先问问自己 2t+3t 的结果是什么？
答案是 5t，因为在这两个数字中存在相同的变量“t”，因此我们将两个数字的系数相加，即 2,3，并将变量“t”附加到结果中。
这里同样在进行加法时，我们需要检查 10 的幂是否相同。
第 1 步：这里两个数字的 10 次方相同，即 2。如果 10 次方相同，则跳过第 2 步直接进入第 3 步
步骤 2：如果 10 的幂不相同，则转换数字，使两个数的 10 的幂变得相同。
第 3 步：简单地添加系数并附加幂。
2+3 = 5 × 10 2
为了获得更多关于这个添加的内容，让我们做一些例子。
示例 1：在 4 × 10 3和 5 × 10 2之间执行加法。
解决方案：
4 × 103 + 5 × 102
Step 1: Here the powers of 10 for the two numbers are not same. So we need to convert those powers into same either by increasing the one or by decreasing the other.
Step 2: Here we increase the power of second number by decreasing the coefficient.
5 × 102 can be converted to 0.5 × 103
Step 3: As the powers of 10 for two numbers are same now we can add the coefficient part to get the result.
4 × 103 + 0.5 × 103 = 4.5 × 103
示例 2：在 11 × 10 2和 5 × 10 5之间进行加法运算。
解决方案：
11 × 102 + 5 × 105
Step 1: Here the powers of 10 for the two numbers are not same. So we need to convert those powers into same either by increasing the one or by decreasing the other.
Step 2: Here we increase the power of first number from 2 to 5 by decreasing the coefficient.
11 × 102 => 1.1 × 103 => 0.11 × 104 => 0.011 × 105
11 × 102 can be converted to 0.011 × 105
Step 3: As the powers of 10 for two numbers are same now we can add the coefficient part to get the result.
0.011 × 105 + 5 × 105 = 5.011 × 105
科学计数法中的减法
我们可以通过执行加法时遵循的步骤来执行以科学计数法表示的任何数字之间的减法。
让我们看几个例子
示例 1：在 5 × 10 3和 2 × 10 3之间执行减法。
解决方案：
5 × 103 – 2 × 103
Step 1: Here the powers of 10 for the two numbers are same. So we can skip the step-2 part and move to step-3 and perform subtraction between coefficients.
Step 2: Equal powers of 10 if not equal.
Step 3: As the powers of 10 for two numbers are same no we can subtract the coefficient parts to get the result.
5 × 103 – 2 × 103 = 3 × 103
示例 2：求 1 × 10 3 – 2 × 10 2的值
解决方案：
Step 1: Here the powers of 10 for the two numbers are not same. So we need to increment / decrement the power of 10 such that both powers should be equal.
Step 2: Here we decrement the power of first number represented in scientific notation from power of 3 to power of 2 by incrementing the coefficient.
1 × 103 => 10 × 102
Step 3: As the powers of 10 for two numbers are same no we can subtract the coefficient parts to get the result.
10 × 102 – 2 × 102 = 8 × 102
示例 3：求 12 × 10 4 – 4 × 10 5的值
解决方案：
Step 1: Here the powers of 10 for the two numbers are not same. So we need to increment / decrement the power of 10 such that both powers should be equal.
Step 2: Here we decrement the power of second number represented in scientific notation from power of 5 to power of 4 by incrementing the coefficient.
4 × 105 => 40 × 104
Step 3: As the powers of 10 for two numbers are same no we can subtract the coefficient parts to get the result.
12 × 104 – 40 × 104 => -28 × 104 => -2.8 × 105