Math Problem Statement

Simplify the expression (9.6 × 10^(-8)) ÷ (2 × 10^(-15)). Express your answer in scientific notation.

Solution

The problem asks to simplify the expression (9.6×108)÷(2×1015)(9.6 \times 10^{-8}) \div (2 \times 10^{-15}) and express the answer in scientific notation.

Steps to solve:

  1. Divide the coefficients: 9.62=4.8\frac{9.6}{2} = 4.8

  2. Apply the law of exponents for the powers of 10: 108÷1015=108(15)=10710^{-8} \div 10^{-15} = 10^{-8 - (-15)} = 10^{7}

  3. Combine the results: 4.8×1074.8 \times 10^{7}

Thus, the simplified expression in scientific notation is: 4.8×1074.8 \times 10^{7}

Let me know if you need more details or clarifications. Here are 5 related questions for practice:

  1. What is (5×106)÷(1×109)(5 \times 10^{-6}) \div (1 \times 10^{-9}) in scientific notation?
  2. How do you multiply two numbers in scientific notation?
  3. Simplify (1.2×105)×(3×103)(1.2 \times 10^{5}) \times (3 \times 10^{-3}).
  4. What is the general rule for dividing numbers in scientific notation?
  5. How can you express (8×104)×(2×102)(8 \times 10^{4}) \times (2 \times 10^{-2}) in standard form?

Tip: Always apply exponent rules carefully when dealing with multiplication and division in scientific notation.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponents
Division of Powers of 10

Formulas

a × 10^b ÷ c × 10^d = (a ÷ c) × 10^(b - d)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 8-10