Question

Perform the following conversions. a) \(17.8 \mu \mathrm{g}\) to grams b) \(7.22 \times 10^{2} \mathrm{~kg}\) to grams c) \(0.00118 \mathrm{~g}\) to nanograms

Short answer

a) 0.0000178 g, b) 722000 g, c) 1180000 ng

Step-by-step solution

Convert Micrograms to Grams

To convert micrograms to grams, use the conversion factor that 1 microgram (\(1 \, \mu\mathrm{g}\)) is equal to \(10^{-6}\) grams. So, multiply 17.8 micrograms by \(10^{-6}\).\[17.8 \, \mu\mathrm{g} = 17.8 \times 10^{-6} \, \mathrm{g}\]The conversion gives:\[17.8 \, \mu\mathrm{g} = 0.0000178 \, \mathrm{g}\]

Convert Kilograms to Grams

To convert kilograms to grams, use the conversion factor that 1 kilogram (\(1 \, \mathrm{kg}\)) equals 1000 grams. Therefore, multiply\(7.22 \times 10^{2} \, \mathrm{kg}\) by 1000.\[7.22 \times 10^{2} \, \mathrm{kg} = 7.22 \times 10^{2} \times 1000 \, \mathrm{g}\]This simplifies to:\[7.22 \times 10^{2} \, \mathrm{kg} = 7.22 \times 10^{5} \, \mathrm{g}\]Thus,\[7.22 \times 10^{2} \, \mathrm{kg} = 722000 \, \mathrm{g}\]

Convert Grams to Nanograms

To convert grams to nanograms, use the conversion factor that 1 gram (\(1 \, \mathrm{g}\)) is equal to \(10^{9}\) nanograms. Therefore, multiply \(0.00118 \, \mathrm{g}\) by \(10^{9}\).\[0.00118 \, \mathrm{g} = 0.00118 \times 10^{9} \, \mathrm{ng}\]This gives:\[0.00118 \, \mathrm{g} = 1.18 \times 10^{6} \, \mathrm{ng}\]Thus,\[0.00118 \, \mathrm{g} = 1180000 \, \mathrm{ng}\]

Key concepts

Converting Micrograms to Grams

Converting units can sometimes seem complex, but breaking it down into simple steps makes it easier. When you want to convert micrograms to grams, it is important to understand the relationship between these two units.

• 1 microgram (\( \, \mu\mathrm{g} \, \) ) is equal to \( \, 10^{-6} \, \) grams (g).
• This means that one microgram is one millionth of a gram.

To convert 17.8 micrograms to grams, you simply multiply 17.8 by \( \, 10^{-6} \, \) to switch from a smaller unit to a larger one:

\[17.8 \, \mu\mathrm{g} = 17.8 \times 10^{-6} \, \mathrm{g} = 0.0000178 \, \mathrm{g}\]Understanding this method ensures that you can easily convert any given quantity of micrograms to grams whenever needed.

Converting Kilograms to Grams

Kilograms and grams are part of the metric system, which is based on powers of ten. This makes it super straightforward to convert between them. The key thing to remember is:

• 1 kilogram (kg) equals 1000 grams (g).
• Think of kilograms as heavier, so you multiply to get the lighter grams.

For instance, converting \( \, 7.22 \times 10^{2} \, \mathrm{kg} \, \) to grams involves multiplying by 1000:

\[7.22 \times 10^{2} \, \mathrm{kg} = 7.22 \times 10^{2} \times 1000 \, \mathrm{g}\]This simplifies to:\[722000 \, \mathrm{g}\]This shows the ease with which you can scale up using the metric system’s base-ten logic. Thus, by multiplying by 1000, you correctly convert kilograms to grams.

Converting Grams to Nanograms

Converting grams to nanograms involves using scientific notation due to the vast difference in these units. Here’s a breakdown of what to know:

• 1 gram (g) is equal to \( \, 10^{9} \, \) nanograms (ng).
• Think of nanograms as incredibly tiny (one-billionth of a gram).

Let's look at how to convert \( \, 0.00118 \, \mathrm{g} \, \) to nanograms:First, multiply 0.00118 by \( \, 10^{9} \, \) to switch from a larger unit to a much smaller one:

\[0.00118 \, \mathrm{g} = 0.00118 \times 10^{9} \, \mathrm{ng} = 1180000 \, \mathrm{ng}\]Thus, by using the conversion factor of \( \, 10^{9} \, \) and multiplying, you can quickly convert grams into nanograms. This process reveals how unit conversions can bridge vastly different scales while maintaining accuracy.