Question

In 2013 the Los Angeles Dodgers opening day payroll was about $2.16 x 108and the Houston Astros opening day
payroll was about $2.4 x 107.
How much higher was the Dodgers’ payroll?



How many times higher is the Dodgers payroll?

Answer 1

To find how much higher the Dodgers’ payroll was compared to the Astros’ payroll, we can subtract the Astros' payroll from the Dodgers' payroll.

### Step 1: Convert the payrolls into standard form for easier calculation.

- Dodgers' payroll: \(2.16 \times 10^8\)
- Astros' payroll: \(2.4 \times 10^7\)

### Step 2: Convert Astros' payroll to the same power of ten as the Dodgers' payroll.

To make the comparison easier, we can express the Astros' payroll in terms of \(10^8\):
\[
2.4 \times 10^7 = 0.24 \times 10^8
\]

### Step 3: Subtract the two payrolls.

Now we can subtract:
\[
\text{Difference} = (2.16 \times 10^8) - (0.24 \times 10^8) = (2.16 - 0.24) \times 10^8 = 1.92 \times 10^8
\]

### Step 4: Calculate how many times higher the Dodgers' payroll is than the Astros' payroll.

To find how many times higher the Dodgers' payroll is, we divide the Dodgers' payroll by the Astros' payroll:
\[
\text{Times higher} = \frac{2.16 \times 10^8}{2.4 \times 10^7}
\]

We can simplify this:
\[
\frac{2.16}{2.4} = 0.9 \quad \text{and} \quad \frac{10^8}{10^7} = 10^{8-7} = 10^1
\]
Thus,
\[
\text{Times higher} = 0.9 \times 10^1 = 9
\]

### Summary:
- The Dodgers’ payroll was \(1.92 \times 10^8\) higher than the Astros' payroll.
- The Dodgers’ payroll was 9 times higher than the Astros' payroll.