The value of 3.00 km in yards upto correct significant figures and the scientific notation is, (1m = 1.094 yards)

Options

A. 3282
B. `32.8X10^2`
C. `3.28X10^3`
D. `328.2X10^1`

Answer

To convert 3.00 kilometers to yards, we follow these steps:

### Step 1: Convert kilometers to meters
1 kilometer is equal to 1,000 meters. Therefore, to convert 3.00 kilometers to meters:
\[ 3.00 \text{ km} = 3.00 \times 1000 \text{ m} = 3000 \text{ m} \]

### Step 2: Convert meters to yards
We know that 1 meter is equal to 1.094 yards. To convert 3000 meters to yards:
\[ 3000 \text{ m} \times 1.094 \text{ yards/m} = 3282 \text{ yards} \]

### Step 3: Determine significant figures
The original value of 3.00 km has three significant figures (the digits 3, 0, and 0). Therefore, we need to express our final answer in three significant figures.

### Step 4: Express the answer in scientific notation
To express 3282 in scientific notation:
\[ 3282 = 3.282 \times 10^3 \]
However, since we need to round to three significant figures, we take:
\[ 3.282 \text{ rounded to three significant figures is } 3.28 \]
Thus, we write:
\[ 3282 \text{ yards} = 3.28 \times 10^3 \text{ yards} \]

### Final Answer
The value of 3.00 km in yards, expressed with the correct significant figures and in scientific notation, is:
\[ \boxed{3.28 \times 10^3 \text{ yards}} \]

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