Addition and Subtraction in Scientific Notation
Last Updated : 06 Jan, 2024
Scientific notation is a way to represent large and smaller numbers in easy representation form. Any number can be represented in this scientific notation such that the number is in between 1 (one) and 10 (ten) and is multiplied by the power of 10.
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.
Addition in Scientific notation
We can perform addition between two or more numbers represented in scientific notation. To explain the way to perform addition in scientific notation consider an example
2 × 102 + 3 × 102
Before going to solve the above problem just question yourself what is the result of 2t+3t?
The answer is 5t because in those two numbers there is the same variable 't' so we add the coefficient of two numbers i.e., 2,3 and append the variable 't' to the result.
Here also while performing addition we need to check whether the power of 10 is the same or not.
Step 1: Here the power of 10 for both the numbers are the same i.e., 2. If powers of 10 are the same then move to Step 3 directly by skipping Step 2
Step 2: If powers of 10 are not the same then convert the number such that the power of 10 of two numbers become the same.
Step 3: Simply add coefficients and append the powers.
2+3 = 5 × 102
To get more coverage on this addition let's do some examples.
Example 1: Perform addition between 4 × 103 and 5 × 102.
Solution:
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
Example 2: Perform addition between 11 × 102 and 5 × 105.
Solution:
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
Subtraction in Scientific Notation
We can perform the subtraction between/among any numbers represented in scientific notation by the steps which are followed while performing addition.
Let us look at a few examples
Example 1: Perform subtraction between 5 × 103 and 2 × 103.
Solution:
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
Example 2: Find the value of 1 × 103 - 2 × 102
Solution:
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
Example 3: Find the value of 12 × 104 - 4 × 105
Solution:
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