Sure! Let's break down the problem step-by-step.
The expression we need to evaluate is:
[tex]\[
\frac{5.1 \times 10^5 + 1.4 \times 10^4}{3.5 \times 10^{-4}}
\][/tex]
### Step 1: Calculate the Numerator
First, we need to add the two numbers in the numerator:
[tex]\[
5.1 \times 10^5 + 1.4 \times 10^4
\][/tex]
Given:
[tex]\[
5.1 \times 10^5 = 510000 \quad \text{(or more precise 509999.99999999994)}
\][/tex]
[tex]\[
1.4 \times 10^4 = 14000
\][/tex]
Adding these values together:
[tex]\[
510000 + 14000 = 524000 \quad \text{(or more precise 523999.99999999994)}
\][/tex]
### Step 2: Calculate the Denominator
We already have the denominator:
[tex]\[
3.5 \times 10^{-4} = 0.00035
\][/tex]
### Step 3: Perform the Division
Now, we divide the sum obtained in the numerator by the denominator:
[tex]\[
\frac{524000}{0.00035}
\][/tex]
By performing the division:
[tex]\[
524000 \div 0.00035 = 1497142857.142857 \quad \text{(approximately)}
\][/tex]
### Step 4: Express the Result in Standard Form
Expressing the result in standard form means writing it as [tex]\( a \times 10^b \)[/tex] where [tex]\( 1 \leq a < 10 \)[/tex].
Here, the result is approximately:
[tex]\[
1497142857.142857
\][/tex]
To convert this to standard form:
[tex]\[
1497142857.142857 = 1.50 \times 10^9 \quad \text{(rounding to 2 significant figures)}
\][/tex]
Thus, the final result is:
[tex]\[
\boxed{1.50 \times 10^9}
\][/tex]
