Certainly! Let's work through this problem step by step.
### Step 1: Multiply the Numerator
First, we have to multiply the two numbers in the numerator:
[tex]\[
4.67 \times 10^{-5} \times 6.98 \times 10^{12}
\][/tex]
This involves multiplying the coefficients (4.67 and 6.98) and adding the exponents (-5 and 12) of the powers of 10:
[tex]\[
(4.67 \times 6.98) \times 10^{-5 + 12}
\][/tex]
Calculating the coefficient:
[tex]\[
4.67 \times 6.98 = 32.5966
\][/tex]
And adding the exponents:
[tex]\[
-5 + 12 = 7
\][/tex]
So, the numerator simplifies to:
[tex]\[
32.5966 \times 10^7
\][/tex]
### Step 2: Writing the Denominator in Standard Form
The denominator is already given in standard form:
[tex]\[
5.04 \times 10^3
\][/tex]
### Step 3: Perform the Division
Next, we divide the result of the numerator by the denominator:
[tex]\[
\frac{32.5966 \times 10^7}{5.04 \times 10^3}
\][/tex]
This can be broken into dividing the coefficients and subtracting the exponents of the powers of 10:
[tex]\[
\frac{32.5966}{5.04} \times 10^{7-3}
\][/tex]
Calculating the coefficient:
[tex]\[
\frac{32.5966}{5.04} = 6.4675
\][/tex]
And subtracting the exponents:
[tex]\[
7 - 3 = 4
\][/tex]
So, the result of the division simplifies to:
[tex]\[
6.4675 \times 10^4
\][/tex]
### Step 4: Round to 3 Significant Figures
To express the result in standard form with 3 significant figures, we round 6.4675 to 3 significant figures:
[tex]\[
6.4675 \approx 6.47
\][/tex]
So, our final answer in standard form with 3 significant figures is:
[tex]\[
6.47 \times 10^4
\][/tex]
### Conclusion
Thus, the value of
[tex]\[
\frac{4.67 \times 10^{-5} \times 6.98 \times 10^{12}}{5.04 \times 10^3}
\][/tex]
in standard form to 3 significant figures is:
[tex]\[
6.47 \times 10^4
\][/tex]
