Which value is closest to the mass of a 2-pound box of laundry detergent?
A. $2.0 \times 10^{-4} cg$
B. 200 g
C. 1 kg
D. $9 \times 10^9 mg$
E. $4.5 \times 10^3 ng$
Answer (1)
Convert 2 pounds to grams: 2 l b ≈ 907.184 g .
Convert all given values to grams: 2.0 × 1 0 − 4 c g = 2.0 × 1 0 − 6 g , 200 g = 200 g , 1 k g = 1000 g , 9 × 1 0 9 m g = 9 , 000 , 000 g , 4.5 × 1 0 3 n g = 4.5 × 1 0 − 6 g .
Calculate the absolute differences between each value and 907.184 g.
The smallest difference is 92.816, corresponding to 1 kg. Therefore, the closest value is 1 k g .
Explanation
Convert pounds to grams We need to determine which of the given values is closest to the mass of a 2-pound box of laundry detergent. First, let's convert 2 pounds to grams. We know that 1 pound is approximately 0.453592 kilograms, and 1 kilogram is 1000 grams. Therefore, 2 pounds is approximately 2 l b × 0.453592 k g / l b × 1000 g / k g = 907.184 g .
Convert all values to grams Now, let's convert all the given values to grams:
2.0 × 1 0 − 4 c g = 2.0 × 1 0 − 4 × 0.01 g = 2.0 × 1 0 − 6 g
200 g = 200 g
1 k g = 1000 g
9 × 1 0 9 m g = 9 × 1 0 9 × 0.001 g = 9 × 1 0 6 g = 9 , 000 , 000 g
4.5 × 1 0 3 n g = 4.5 × 1 0 3 × 1 0 − 9 g = 4.5 × 1 0 − 6 g
Calculate the absolute differences Now, we calculate the absolute difference between each value and the mass of the 2-pound box in grams (907.184 g):
∣907.184 − 2.0 × 1 0 − 6 ∣ = 907.183998
∣907.184 − 200∣ = 707.184
∣907.184 − 1000∣ = 92.816
∣907.184 − 9 , 000 , 000∣ = 8 , 092 , 816
∣907.184 − 4.5 × 1 0 − 6 ∣ = 907.1839955
Find the minimum absolute difference The smallest absolute difference is 92.816, which corresponds to the value 1 kg. Therefore, the value closest to the mass of a 2-pound box of laundry detergent is 1 kg.
Examples
Understanding mass and unit conversions is crucial in everyday life. For example, when following a recipe, you might need to convert ounces to grams. Knowing these conversions helps in accurate measurements, ensuring the recipe turns out as expected. Similarly, in construction or engineering, converting between pounds and kilograms is essential for calculating loads and ensuring structural integrity.
