-x-(4.9-x-10%5E-5)-in-scientific-notation.jpeg "(7.7 X 10^8) X (4.9 X 10^-5) In Scientific Notation")
Scientific Notation: Simplifying Multiplication of Large Numbers
When dealing with extremely large or small numbers, scientific notation becomes an essential tool for simplifying calculations. In this article, we will explore how to multiply two numbers in scientific notation: (7.7 x 10^8) x (4.9 x 10^-5).
What is Scientific Notation?
Scientific notation is a way of expressing very large or very small numbers in a more compact and readable form. It involves writing a number as a product of a coefficient (a number between 1 and 10) and a power of 10. The general format for scientific notation is:
a x 10^n
where a is the coefficient and n is the exponent.
Multiplying Numbers in Scientific Notation
When multiplying two numbers in scientific notation, we need to follow a simple rule:
(a x 10^n) x (b x 10^m) = (a x b) x 10^(n+m)
In our example, we have:
(7.7 x 10^8) x (4.9 x 10^-5)
To multiply these numbers, we need to follow the rule above:
(7.7 x 4.9) x 10^(8 + -5)
Calculating the Coefficient
First, let's calculate the coefficient by multiplying the two numbers:
7.7 x 4.9 = 37.73
Calculating the Exponent
Next, let's calculate the exponent by adding the two exponents:
8 + -5 = 3
The Final Answer
Now that we have calculated the coefficient and exponent, we can write the final answer in scientific notation:
37.73 x 10^3
Conclusion
In this article, we have demonstrated how to multiply two numbers in scientific notation: (7.7 x 10^8) x (4.9 x 10^-5). By following the simple rule of multiplying the coefficients and adding the exponents, we can simplify complex calculations involving large and small numbers.
