Math Problem Statement

3.96×10^5 / (1.423×10^-2 × 5.883×10^-3) can be written in the form b × 10^n. Write b correct to 2 decimal places and n as an integer.

Solution

The result of the given expression is approximately 4.7303×1094.7303 \times 10^9.

Thus, in the form b×10nb \times 10^n:

  • b=4.73b = 4.73 (correct to 2 decimal places)
  • n=9n = 9 (as an integer).

Would you like more details or have any other questions?

Here are five related questions to explore:

  1. How do you simplify powers of 10 when dividing or multiplying?
  2. How does scientific notation help in simplifying large or small numbers?
  3. What are some real-world applications of scientific notation?
  4. Can you convert 4.7303×1094.7303 \times 10^9 to standard form?
  5. How do you handle negative powers in the denominator?

Tip: When dividing numbers in scientific notation, subtract the exponents of 10.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Division of Powers of 10
Multiplication of Powers of 10

Formulas

Division in Scientific Notation: (a×10^m) / (b×10^n) = (a/b) × 10^(m-n)
Multiplication of Powers of 10: (a×10^m) × (b×10^n) = (a×b) × 10^(m+n)

Theorems

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Suitable Grade Level

Grades 8-10