Simplify the expression (8.5×10−2)×288(1.7×105)×(3.6×104) using scientific notation and express your answer in scientific notation. Round your answer to the nearest thousandth.

To simplify the expression \( \frac{(8.5 \times 10^{-2}) \times 288}{(1.7 \times 10^5) \times (3.6 \times 10^4)} \) and express the answer in scientific notation, follow these steps:

### Step 1: Simplify the expression in the numerator
The numerator is:
\[
(8.5 \times 10^{-2}) \times 288
\]
First, multiply the coefficient:
\[
8.5 \times 288 = 2448
\]
Now, express \( 2448 \) in scientific notation:
\[
2448 = 2.448 \times 10^3
\]
Thus, the numerator becomes:
\[
2.448 \times 10^3 \times 10^{-2} = 2.448 \times 10^{3 - 2} = 2.448 \times 10^1
\]

### Step 2: Simplify the expression in the denominator
The denominator is:
\[
(1.7 \times 10^5) \times (3.6 \times 10^4)
\]
First, multiply the coefficients:
\[
1.7 \times 3.6 = 6.12
\]
Then, add the exponents of 10:
\[
10^5 \times 10^4 = 10^{5 + 4} = 10^9
\]
So, the denominator becomes:
\[
6.12 \times 10^9
\]

### Step 3: Divide the simplified numerator by the simplified denominator
Now divide the numerator by the denominator:
\[
\frac{2.448 \times 10^1}{6.12 \times 10^9} = \frac{2.448}{6.12} \times 10^{1 - 9}
\]
First, divide the coefficients:
\[
\frac{2.448}{6.12} \approx 0.4
\]
Then, subtract the exponents of 10:
\[
10^{1 - 9} = 10^{-8}
\]
So, the expression simplifies to:
\[
0.4 \times 10^{-8} = 4 \times 10^{-9}
\]

### Final Answer
The simplified expression in scientific notation, rounded to the nearest thousandth, is:
\[
\boxed{4.0 \times 10^{-9}}
\]

Would you like more details on any part of this process? 

Here are five related questions you might consider:
1. How do you multiply and divide numbers in scientific notation with negative exponents?
2. How would you express \( 0.00056 \) in scientific notation?
3. What is the result of \( (4.2 \times 10^3) \times (2 \times 10^{-5}) \)?
4. How do you add and subtract numbers in scientific notation?
5. What is the value of \( \frac{6.4 \times 10^7}{8 \times 10^{-2}} \)?

**Tip:** When dividing numbers in scientific notation, divide the coefficients and subtract the exponents.

Learn how to simplify the expression (8.5×10−2)×288(1.7×105)×(3.6×104) using scientific notation. Follow a step-by-step solution to multiply and divide numbers in scientific notation with negative exponents. Suitable for high school students studying scientific notation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation