Perform the indicated operation and write the answer in decimal notation.$(3\times {10}^3)(1.3\times {10}^2)$

Verified step by step guidance

1. Identify the given expression: \( (3 \times 10^{3}) (1.3 \times 10^{2}) \). This is a multiplication of two numbers expressed in scientific notation.
2. Use the property of exponents and multiplication: when multiplying numbers in scientific notation, multiply the coefficients (the numbers in front) and add the exponents of 10. So, multiply 3 and 1.3, and add the exponents 3 and 2.
3. Calculate the product of the coefficients: \(3 \times 1.3\).
4. Add the exponents of 10: \$3 + 2$ to get the new exponent.
5. Combine the results to write the product in scientific notation, then convert this scientific notation to decimal notation by moving the decimal point according to the exponent.

Key Concepts

Scientific Notation

Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10. It simplifies working with very large or small numbers by using exponents, such as 3 × 10^3 representing 3000.

Multiplication of Numbers in Scientific Notation

When multiplying numbers in scientific notation, multiply the decimal parts and add the exponents of 10. For example, (3 × 10^3)(1.3 × 10^2) equals (3 × 1.3) × 10^(3+2).

Conversion to Decimal Notation

After performing operations in scientific notation, convert the result to decimal notation by calculating the power of 10 and multiplying it by the decimal number. This gives the final answer in standard numerical form.