The total area of a particular country is 32500000 square miles. Which of the following expressions represents the area in scientific notation?

Options

A. `(3.25 xx 10^7)` sq. miles
B. `(325 xx 10^5)` sq. miles
C. `(32.5 xx 10^6)` sq. miles
D. `(3.25 xx 10^6)` sq. miles

Answer

To express the total area of the country, which is 32,500,000 square miles, in scientific notation, we can follow these steps:

### Step 1: Identify the significant digits
The significant digits in the number 32,500,000 are 3, 2, and 5.

### Step 2: Place the decimal point
To convert this number into scientific notation, we need to place the decimal point after the first significant digit. This gives us:
\[ 3.25 \]

### Step 3: Count the number of places the decimal point has moved
The original number is 32,500,000. The decimal point in 3.25 was moved 7 places to the left to get back to the original number.

### Step 4: Write the number in scientific notation
In scientific notation, we express the number as:
\[ 3.25 \times 10^7 \]

### Step 5: Include the units
Since the area is given in square miles, we write:
\[ 3.25 \times 10^7 \text{ square miles} \]

Thus, the expression representing the area in scientific notation is:
\[ 3.25 \times 10^7 \text{ square miles} \]