Simplify and express in scientific notation: (1.247 × 10–3) ÷ (2.9 × 10–2)

To simplify and express the given expression in scientific notation, we follow these steps:

Given:

\[
\text{Expression} = \frac{1.247 \times 10^{-3}}{2.9 \times 10^{-2}}
\]

### Step 1: Simplify the numerical coefficients

Divide the numerical coefficients:

\[
\frac{1.247}{2.9} \approx 0.430
\]

### Step 2: Simplify the powers of 10

Subtract the exponents (since we are dividing):

\[
10^{-3} \div 10^{-2} = 10^{-3 - (-2)} = 10^{-3 + 2} = 10^{-1}
\]

### Step 3: Combine the results

Now, multiply the simplified numerical coefficient by the power of 10:

\[
0.430 \times 10^{-1}
\]

### Step 4: Express in scientific notation

To express this in proper scientific notation, we need to adjust the coefficient so that it is between 1 and 10:

\[
0.430 \times 10^{-1} = 4.30 \times 10^{-2}
\]

Thus, the simplified expression in scientific notation is:

\[
\boxed{4.30 \times 10^{-2}}
\]

Would you like further explanation or any additional questions? Here are 8 related questions you might find interesting:

1. How do you simplify expressions with negative exponents?
2. What is the significance of scientific notation in calculations?
3. How would you handle a similar problem with different exponents?
4. What are the steps to convert any decimal number into scientific notation?
5. How do you multiply and divide numbers in scientific notation?
6. What is the importance of keeping the coefficient between 1 and 10 in scientific notation?
7. How do operations on numbers in scientific notation differ from those in standard form?
8. How would you express \(0.045\) in scientific notation?

**Tip:** When dealing with scientific notation, always adjust the coefficient to fall between 1 and 10 for proper representation.

Learn how to simplify and express the division of numbers in scientific notation. This problem covers converting expressions into scientific notation, dividing numbers with negative exponents, and adjusting coefficients for proper scientific notation representation. 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