[(58.6)(1.2 x 10-5) – (2.08 x 10-4) (1801)] / 4.6944 x 10-5

Let's break down the expression step by step.

The expression is:

\[
\frac{(58.6)(1.2 \times 10^{-5}) - (2.08 \times 10^{-4})(1801)}{4.6944 \times 10^{-5}}
\]

### Step 1: Multiply the terms inside the parentheses.

1. \( (58.6)(1.2 \times 10^{-5}) = 58.6 \times 1.2 \times 10^{-5} = 70.32 \times 10^{-5} = 7.032 \times 10^{-4} \)
2. \( (2.08 \times 10^{-4})(1801) = 2.08 \times 1801 \times 10^{-4} = 3745.08 \times 10^{-4} = 3.74508 \times 10^{-1} \)

### Step 2: Subtract the results from the two products.

\[
7.032 \times 10^{-4} - 3.74508 \times 10^{-1}
\]

Since \( 3.74508 \times 10^{-1} \) is much larger than \( 7.032 \times 10^{-4} \), we approximate:

\[
7.032 \times 10^{-4} - 3.74508 \times 10^{-1} \approx -3.745072968 \times 10^{-1}
\]

### Step 3: Divide by \( 4.6944 \times 10^{-5} \).

\[
\frac{-3.745072968 \times 10^{-1}}{4.6944 \times 10^{-5}} \approx -7977.94
\]

### Final Answer:
\[
\approx -7977.94
\]

Would you like more details, or do you have any questions?

### Related Questions:
1. How can scientific notation simplify large or small number calculations?
2. What are some common pitfalls when working with scientific notation in arithmetic?
3. How do you handle operations involving different powers of ten?
4. How does changing the order of operations affect the outcome in complex expressions?
5. What are some strategies for checking the accuracy of calculations involving scientific notation?

### Tip:
When working with numbers in scientific notation, always pay close attention to the exponents as they can significantly impact the result.

Learn how to solve a complex arithmetic problem involving scientific notation. This problem covers operations with large and small numbers in scientific notation, including multiplication, subtraction, and division. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation