Question

question 4 (5 points) which of the following mass is the largest? 8.2 × 10³ dg 8.2 cg 0.082 g 8.2 × 10⁹ μg 8.2 × 10⁻⁶ mg

Explanation:

Step1: Convert all units to grams (g)

• For \(8.2 \times 10^{3}\space \text{dg}\):

Since \(1\space \text{dg} = 0.1\space \text{g}\), then \(8.2 \times 10^{3}\space \text{dg}=8.2 \times 10^{3}\times0.1\space \text{g}=8.2 \times 10^{2}\space \text{g} = 820\space \text{g}\).

• For \(8.2\space \text{cg}\):

Since \(1\space \text{cg} = 0.01\space \text{g}\), then \(8.2\space \text{cg}=8.2\times0.01\space \text{g}=0.082\space \text{g}\).

• For \(0.082\space \text{g}\):

It is already in grams, so it is \(0.082\space \text{g}\).

• For \(8.2 \times 10^{9}\space \mu\text{g}\):

Since \(1\space \mu\text{g} = 10^{-6}\space \text{g}\), then \(8.2 \times 10^{9}\space \mu\text{g}=8.2 \times 10^{9}\times10^{-6}\space \text{g}=8.2 \times 10^{3}\space \text{g}=8200\space \text{g}\).

• For \(8.2 \times 10^{-6}\space \text{Mg}\):

Since \(1\space \text{Mg} = 10^{6}\space \text{g}\), then \(8.2 \times 10^{-6}\space \text{Mg}=8.2 \times 10^{-6}\times10^{6}\space \text{g}=8.2\space \text{g}\).

Step2: Compare the values

• \(8.2 \times 10^{3}\space \text{dg} = 820\space \text{g}\)
• \(8.2\space \text{cg} = 0.082\space \text{g}\)
• \(0.082\space \text{g}\)
• \(8.2 \times 10^{9}\space \mu\text{g} = 8200\space \text{g}\)
• \(8.2 \times 10^{-6}\space \text{Mg} = 8.2\space \text{g}\)

By comparing these values (\(8200\space \text{g} > 820\space \text{g} > 8.2\space \text{g} > 0.082\space \text{g}\)), we can see that \(8.2 \times 10^{9}\space \mu\text{g}\) is the largest.

Answer:

\(8.2 \times 10^{9}\space \mu\text{g}\) (the option with the radio button selected in the original problem, which is correct after unit conversion comparison)