Math Problem Statement

2.993 x 10^10 / 2 x 10^-6

Solution

To solve the expression 2.993×10102×106\frac{2.993 \times 10^{10}}{2 \times 10^{-6}}, we follow these steps:

Step 1: Simplify the numbers

We can rewrite the expression as: 2.993×10102×106=2.9932×1010106\frac{2.993 \times 10^{10}}{2 \times 10^{-6}} = \frac{2.993}{2} \times \frac{10^{10}}{10^{-6}} 2.9932=1.4965\frac{2.993}{2} = 1.4965

Step 2: Simplify the powers of 10

1010106=1010(6)=1016\frac{10^{10}}{10^{-6}} = 10^{10 - (-6)} = 10^{16}

Step 3: Combine the results

1.4965×1016=1.4965×10161.4965 \times 10^{16} = 1.4965 \times 10^{16}

So, the final answer is: 1.4965×10161.4965 \times 10^{16}

Would you like further details or clarification on any step?

Here are 5 related questions you might find useful:

  1. How do you multiply or divide numbers in scientific notation?
  2. What are the rules for adding or subtracting exponents in division and multiplication?
  3. How do you convert a large number into scientific notation?
  4. What are the applications of scientific notation in physics and engineering?
  5. How can you use a calculator to simplify scientific notation problems?

Tip: When dividing numbers in scientific notation, focus on simplifying both the coefficients and the exponents separately to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponent Rules
Division of Powers of Ten

Formulas

a^m / a^n = a^(m - n)
Multiplying and dividing coefficients in scientific notation

Theorems

Laws of Exponents

Suitable Grade Level

Grades 9-12