Perform the indicated operation and write the answer in decimal notation. (3*10^3)(1.3*10^2)

Key Concepts

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form. It is written as a product of a number between 1 and 10 and a power of ten. For example, 3 * 10^3 represents 3000. Understanding this notation is essential for performing operations involving large numbers efficiently.

Multiplication of Exponents

When multiplying numbers in scientific notation, you multiply the coefficients and add the exponents of the powers of ten. For instance, in the expression (3 * 10^3)(1.3 * 10^2), you multiply 3 by 1.3 and add the exponents 3 and 2, resulting in a new power of ten. This property simplifies calculations significantly.

Decimal Notation

Decimal notation is the standard way of writing numbers using digits 0-9, where the position of each digit represents a power of ten. Converting from scientific notation to decimal notation involves calculating the value of the number based on its exponent. For example, converting 6.9 * 10^5 to decimal notation results in 690000.