-%2B-(5-x-10%5E5)-in-scientific-notation.jpeg "(2 X 10^3) + (5 X 10^5) In Scientific Notation")
Adding Numbers in Scientific Notation: (2 x 10^3) + (5 x 10^5)
This article explores how to add numbers written in scientific notation, using the example of (2 x 10^3) + (5 x 10^5).
Understanding Scientific Notation
Scientific notation is a way of writing very large or very small numbers in a concise and convenient form. It follows the format:
a x 10^b
where:
- a is a number between 1 and 10 (often referred to as the coefficient)
- b is an integer (positive or negative) representing the power of 10.
The Steps to Add Numbers in Scientific Notation
-
Ensure the exponents are the same. If the exponents are different, adjust the smaller exponent to match the larger one.
In our example, we need to adjust 10^3 to 10^5:
(2 x 10^3) = (2 x 10^(3-2) x 10^5) = (0.02 x 10^5)
-
Add the coefficients.
(0.02 x 10^5) + (5 x 10^5) = (0.02 + 5) x 10^5
-
Simplify the result.
(0.02 + 5) x 10^5 = 5.02 x 10^5
Conclusion
Therefore, the sum of (2 x 10^3) + (5 x 10^5) is 5.02 x 10^5. This demonstrates the process of adding numbers in scientific notation, ensuring the exponents are consistent and then adding the coefficients.