https://file.aiquickdraw.com/mathbot/file/1727797466925xr9vt452.jpg

Let's break down the expression and solve it step by step.

The given expression is:

\[
\frac{(3.56 \times 10^{-5}) \times (5.87 \times 10^{12})}{4.03 \times 10^3}
\]

### Step 1: Multiply the terms in the numerator

\[
(3.56 \times 10^{-5}) \times (5.87 \times 10^{12}) = 3.56 \times 5.87 \times 10^{-5 + 12}
\]

Calculate the multiplication of the constants:

\[
3.56 \times 5.87 = 20.8972
\]

Now simplify the powers of 10:

\[
10^{-5 + 12} = 10^7
\]

So the numerator becomes:

\[
20.8972 \times 10^7
\]

### Step 2: Divide by the denominator

Now divide the result by \( 4.03 \times 10^3 \):

\[
\frac{20.8972 \times 10^7}{4.03 \times 10^3} = \frac{20.8972}{4.03} \times 10^{7 - 3}
\]

Calculate the division of the constants:

\[
\frac{20.8972}{4.03} \approx 5.186
\]

Now simplify the powers of 10:

\[
10^{7 - 3} = 10^4
\]

So the result is:

\[
5.186 \times 10^4
\]

### Step 3: Round to 3 significant figures

Rounding \( 5.186 \times 10^4 \) to 3 significant figures:

\[
5.19 \times 10^4
\]

### Final Answer:

The answer in standard form to 3 significant figures is:

\[
5.19 \times 10^4
\]

---

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you multiply and divide numbers in scientific notation?
2. What are significant figures and how do you round numbers to them?
3. Can you explain how powers of 10 are manipulated during multiplication and division?
4. How do you convert between standard form and scientific notation?
5. How does the use of a calculator simplify complex operations involving scientific notation?

**Tip:** When working with scientific notation, it's often helpful to first handle the powers of 10 separately before combining them with the base numbers.

Use a calculator to work out (3.56 × 10^-5) × (5.87 × 10^12) ÷ (4.03 × 10^3). Give your answer in standard form to 3 significant figures.

Learn how to solve the scientific notation problem involving multiplication and division of powers of 10. The final result is expressed in standard form with 3 significant figures.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation