Math Problem Statement

Evaluate the following product. Leave your answer in scientific notation.  

(5.2×103)(2.7×10−9)

Solution

To evaluate the product (5.2×103)×(2.7×109)(5.2 \times 10^3) \times (2.7 \times 10^{-9}), follow these steps:

  1. Multiply the coefficients:
    5.2×2.7=14.045.2 \times 2.7 = 14.04

  2. Add the exponents of 10:
    103×109=103+(9)=10610^3 \times 10^{-9} = 10^{3 + (-9)} = 10^{-6}

  3. Combine the results:
    14.04×10614.04 \times 10^{-6}

Since scientific notation requires the coefficient to be between 1 and 10, adjust 14.04×10614.04 \times 10^{-6} as follows:

14.04×106=1.404×10514.04 \times 10^{-6} = 1.404 \times 10^{-5}

Thus, the answer in scientific notation is:

1.404×105\boxed{1.404 \times 10^{-5}}

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

  1. How do you handle multiplication when one number is not in scientific notation?
  2. What steps are needed to adjust a coefficient in scientific notation to be between 1 and 10?
  3. How does adding the exponents work when multiplying powers of 10?
  4. What if the coefficient multiplication gives a value less than 1?
  5. How do you convert very large or very small numbers into scientific notation?

Tip: When multiplying numbers in scientific notation, always check if the coefficient needs adjusting to keep it between 1 and 10.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Multiplication of Numbers in Scientific Notation

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12