Addition and Subtraction in Scientific Notation

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