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Subtracting Scientific Notation

Subtracting numbers in scientific notation can be done in few ways.

One way is to change the numbers out of scientific notation and work the problem normally.

Example: change 9.3 x 103 - 8.63 x 102 into 9300 - 863. Then we subtract normally to get 8.437 x 103.

Its an simplest way of working when the numbers are not very large or not very small.

Scientific notation is a form, where the scientific terms that expressing very large or very small numbers in an easiest form. Numbers written in scientific notation can be used in computations (x, ÷, +, –) with ease. Writing the numbers in the form of K x m n is called as scientific notation, which is also known as exponential notation.

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How to Subtract Scientific Notation

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The following are the steps involved in Subtracting Numbers with Scientific Notation

Step 1: Adjust the coefficient of both the numbers to make exponent equal for both the numbers. (It is better to easily adjust the smaller index to equal the larger index).

Step 2: Now subtract the smaller coefficient from the larger coefficient of the numbers.

Step 3: Write the difference in scientific notation.

Subtracting Scientific Notation Example Problems

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Below are the examples on subtracting numbers using scientific notations:

Solved Examples

Question 1: Subtract scientific notation 2.3 x 10 4 from 4.5 x 10 5
Solution:
 

Step 1: Adjust the co-efficient of both the numbers to make exponent equal for both the numbers.

Here 2.3 x 10 4 having the smaller power.

We can write 2.3 x 10 4 as 0.23 x 10 5

Now 4.5 x 10 5 and 0.23 x 10 5 have the same powers.

Step 2: Subtract the coefficient of 0.23 x 10 5 from the coefficient of 4.5 x 10 5

4.5 x 10 5 - 0.23 x 10 5 = 4.5 - 0.23

= 4.27

Step 3: Writing the result in scientific form

Hence, Subtracting scientific notation 4.5 x 10 5- 2.3 x 10 4 = 4.27 x 105


 

Question 2: Subtract scientific notation 0.625 x 102 from 1.15 x 103
Solution:
 

Step 1: Adjust the coefficient of both the numbers to make exponent equal for both the numbers.

Here 0.625 x 102 having the smaller power. We can 0.625 x 102 as 0.0625 x 10 3

Now, 1.15 x 103 and 0.0625 x 10 3 have same powers.

Step 2: Greater coefficient is 1.15 and lower coefficient is 0.0625, Subtract 0.00625 from 1.15

1.15 - 0.0625 = 1.0875

Step 3: Writing the result in scientific form

1.15 x 103 - 0.625 x 102 = 1.0875 x 103


 

Question 3: Subtract scientific notation 15.2 x 105 from 34.3 x 105
Solution:
 

Step 1: Adjust the coefficient of both the numbers to make exponent equal for both the numbers.

Here, 15.2 x 105 and 34.3 x 105 both has the same power

Step 2: Subtract the coefficient of 15.2 x 105 from the coefficient of 34.3 x 105

34.3 - 15.2 = 19.1

Step 3: Writing the result in scientific form

34.3 x 105 - 15.2 x 105 = 19.1 x 105


 

Practice Problem

Question: Subtract scientific notation 15.2 x 105 from 34.3 x 105
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