how many grams are in a 2.5 pound sample? express your answer in scientific notation with three significant figures. (1 pound=453.592 grams) 2.27×10^3 g, 2.26×10^2g, 2.3×10^3 g, 1.13×10^3 g
The Correct Answer and Explanation is :
To convert 2.5 pounds to grams, we will use the conversion factor where 1 pound = 453.592 grams.
Step 1: Convert pounds to grams
Given that:
[
1 \text{ pound} = 453.592 \text{ grams}
]
We can calculate the weight in grams for a 2.5-pound sample:
[
2.5 \text{ pounds} \times \frac{453.592 \text{ grams}}{1 \text{ pound}} = 1133.98 \text{ grams}
]
Step 2: Round to three significant figures
To express the result in scientific notation with three significant figures, we round 1133.98 grams to three significant figures, which gives:
[
1130 \text{ grams}
]
Now, express this in scientific notation:
[
1130 \text{ grams} = 1.13 \times 10^3 \text{ grams}
]
Answer:
Thus, the correct answer is 1.13 x 10^3 g.
Explanation:
Scientific notation is a way of expressing numbers that are too large or too small in a more compact form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10. The number of significant figures indicates the precision of the value. In this case, we used three significant figures to match the precision of the original problem.
The steps are as follows:
- Convert the units: Convert from pounds to grams by multiplying by the conversion factor (1 pound = 453.592 grams).
- Determine the number in scientific notation: After obtaining the result (1133.98 grams), round it to three significant figures and convert it to scientific notation (1.13 x 10^3 grams).
- Scientific notation: This notation expresses the result in a concise manner and maintains the precision required.
By following these steps, the correct result is obtained, which in this case is 1.13 x 10^3 grams.