Math Problem Statement

Find the product of (3 x 109) and (2 x 109). Write the final answer in scientific notation.

Group of answer choices

6 x 1081

6 x 10018

6 x 1018

6 x 109

Solution

Let's first find the product of (3×109)(3 \times 10^9) and (2×109)(2 \times 10^9).

To calculate this:

(3×109)×(2×109)=(3×2)×(109×109)(3 \times 10^9) \times (2 \times 10^9) = (3 \times 2) \times (10^9 \times 10^9)

This simplifies to:

6×109+9=6×10186 \times 10^{9 + 9} = 6 \times 10^{18}

So, the final answer in scientific notation is:

6×10186 \times 10^{18}

Thus, the correct answer is 6 x 10¹⁸.

Would you like to go over any steps in more detail or have other questions?

Here are some related questions:

  1. How do you multiply numbers in scientific notation?
  2. What is the rule for adding exponents when multiplying powers of 10?
  3. Can scientific notation be used for both very large and very small numbers?
  4. How do you divide numbers in scientific notation?
  5. What is the difference between standard form and scientific notation?

Tip: When multiplying numbers in scientific notation, you multiply the base numbers (the ones in front of the powers of 10) and add the exponents of 10.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponent Rules
Multiplication of Powers of 10

Formulas

(a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n)

Theorems

Laws of Exponents: Product Rule (10^m × 10^n = 10^(m+n))

Suitable Grade Level

Grades 8-10