Math Problem Statement

write the scientist notation 3.6x10^-10/ 2 x 10^-6

Solution

To divide the numbers in scientific notation, follow these steps:

You have the expression:

3.6×10102×106\frac{3.6 \times 10^{-10}}{2 \times 10^{-6}}

Step 1: Divide the coefficients

3.62=1.8\frac{3.6}{2} = 1.8

Step 2: Subtract the exponents of 10

1010÷106=1010(6)=1010+6=10410^{-10} \div 10^{-6} = 10^{-10 - (-6)} = 10^{-10 + 6} = 10^{-4}

Final result:

3.6×10102×106=1.8×104\frac{3.6 \times 10^{-10}}{2 \times 10^{-6}} = 1.8 \times 10^{-4}

So the result in scientific notation is:

1.8×1041.8 \times 10^{-4}

Would you like further clarification or details? Here are 5 related questions you might find interesting:

  1. How do you multiply numbers in scientific notation?
  2. What is the rule for adding and subtracting exponents in scientific notation?
  3. How do you convert a number in scientific notation to standard form?
  4. How do you deal with negative exponents in scientific notation?
  5. What is the significance of using scientific notation in science and engineering?

Tip: When working with scientific notation, always keep track of the exponents when multiplying or dividing; it helps to simplify the calculations!

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Division of Exponents
Arithmetic Operations in Scientific Notation

Formulas

\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}

Theorems

Exponent Rule for Division

Suitable Grade Level

Grades 7-9