Math Problem Statement

3.306 × 10^(-1) × 8.930 × 10^2 / 9.905 × 10^(-3) can be written in the form b × 10^n. Write b correct to 2 decimal places, b = __ and n = __.

Solution

The expression simplifies to approximately 2.980573×1042.980573 \times 10^4.

Now, we can rewrite it in the form b×10nb \times 10^n:

  • b=2.98b = 2.98 (to 2 decimal places)
  • n=4n = 4

Would you like more details or have any questions? Here are five related questions you might consider:

  1. How do you manipulate exponents when multiplying and dividing numbers in scientific notation?
  2. Why is it important to express values in the form b×10nb \times 10^n?
  3. How do you round numbers correctly to a specific decimal place?
  4. What are the rules for simplifying powers of 10 when they are multiplied or divided?
  5. How can you ensure the correct number of significant figures in scientific calculations?

Tip: When multiplying or dividing numbers in scientific notation, handle the coefficients and powers of 10 separately, then combine the results.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponent Rules
Division and Multiplication of Powers of 10

Formulas

a × 10^m × b × 10^n = (a × b) × 10^(m+n)
Division of powers: a × 10^m / b × 10^n = (a / b) × 10^(m-n)

Theorems

Laws of Exponents
Scientific Notation

Suitable Grade Level

Grades 10-12