%2B(5x10%5E5)-in-scientific-notation.jpeg "(2x10^3)+(5x10^5) In Scientific Notation")
Adding Numbers in Scientific Notation: (2x10^3) + (5x10^5)
This article will guide you through the process of adding numbers expressed in scientific notation, using the example of (2x10^3) + (5x10^5).
Understanding Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a compact and convenient form. It follows the format:
a x 10^b
where:
- a is a number between 1 and 10 (the coefficient)
- b is an integer (the exponent)
Adding Numbers in Scientific Notation
To add numbers in scientific notation, the exponents (powers of 10) must be the same. Here's how to approach the problem:
-
Identify the smaller exponent: In our example, the smaller exponent is 3 (in 2x10^3).
-
Adjust the smaller term: To make the exponents match, we need to rewrite 2x10^3 as a number with the exponent 5:
- 2x10^3 = 0.02 x 10^5 (We moved the decimal point two places to the left and decreased the exponent by 2).
-
Add the coefficients: Now we have:
- 0.02 x 10^5 + 5 x 10^5 = 5.02 x 10^5
Conclusion
Therefore, (2x10^3) + (5x10^5) is equal to 5.02 x 10^5 in scientific notation. This process of adjusting the exponents and then adding the coefficients ensures a consistent and accurate calculation.