Questions: In converting 856 mg to hectograms, which of the following conversion setups is incorrect: 856 mg × 10^-2 hg / 1000 mg = 856 mg × 100 hg / 1,000 mg = 856 mg × 1 g / 1000 mg × 1 hg / 100 g = 856 mg × 0.001 g / 1 mg × 10^-2 hg / 1 g = 856 mg × 1 hg / 10^5 mg =

In converting 856 mg to hectograms, which of the following conversion setups is incorrect: 856 mg × 10^-2 hg / 1000 mg = 856 mg × 100 hg / 1,000 mg = 856 mg × 1 g / 1000 mg × 1 hg / 100 g = 856 mg × 0.001 g / 1 mg × 10^-2 hg / 1 g = 856 mg × 1 hg / 10^5 mg =
Transcript text: In converting 856 mg to hectograms, which of the following conversion setups is incorrect: $856 \mathrm{mg} \times \frac{10^{-2} h g}{1000 \mathrm{mg}}=$ $856 \mathrm{mg} \times \frac{100 \mathrm{hg}}{1,000 \mathrm{mg}}=$ $856 \mathrm{mg} \times \frac{1 \mathrm{~g}}{1000 \mathrm{mg}} \times \frac{1 h g}{100 \mathrm{~g}}=$ $856 \mathrm{mg} \times \frac{0.001 \mathrm{~g}}{1 m g} \times \frac{10^{-2} h g}{1 g}=$ $856 \mathrm{mg} \times \frac{1 h g}{10^{5} \mathrm{mg}}=$
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Solution

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Solution Steps

To determine which conversion setup is incorrect, we need to evaluate each setup to see if it correctly converts milligrams (mg) to hectograms (hg). The correct conversion involves converting mg to g and then g to hg. We will check each setup to see if it follows this conversion path correctly.

Step 1: Understand the Conversion Process

To convert milligrams (mg) to hectograms (hg), we need to understand the conversion factors involved:

  1. \(1 \, \text{mg} = 0.001 \, \text{g}\)
  2. \(1 \, \text{hg} = 100 \, \text{g}\)

Thus, to convert from mg to hg, we can use the following conversion factor:

\[ 1 \, \text{mg} = 0.001 \, \text{g} = 0.00001 \, \text{hg} \]

Step 2: Evaluate Each Conversion Setup

Let's evaluate each conversion setup to determine which one is incorrect.

  1. Setup 1: \[ 856 \, \text{mg} \times \frac{10^{-2} \, \text{hg}}{1000 \, \text{mg}} \]

    • This setup implies \(1 \, \text{mg} = 10^{-5} \, \text{hg}\), which is correct.

  2. Setup 2: \[ 856 \, \text{mg} \times \frac{100 \, \text{hg}}{1000 \, \text{mg}} \]

    • This setup implies \(1 \, \text{mg} = 0.1 \, \text{hg}\), which is incorrect.

  3. Setup 3: \[ 856 \, \text{mg} \times \frac{1 \, \text{g}}{1000 \, \text{mg}} \times \frac{1 \, \text{hg}}{100 \, \text{g}} \]

    • This setup implies \(1 \, \text{mg} = 0.00001 \, \text{hg}\), which is correct.

  4. Setup 4: \[ 856 \, \text{mg} \times \frac{0.001 \, \text{g}}{1 \, \text{mg}} \times \frac{10^{-2} \, \text{hg}}{1 \, \text{g}} \]

    • This setup implies \(1 \, \text{mg} = 0.00001 \, \text{hg}\), which is correct.

  5. Setup 5: \[ 856 \, \text{mg} \times \frac{1 \, \text{hg}}{10^{5} \, \text{mg}} \]

    • This setup implies \(1 \, \text{mg} = 0.00001 \, \text{hg}\), which is correct.

Final Answer

The incorrect conversion setup is:

\[ \boxed{856 \, \text{mg} \times \frac{100 \, \text{hg}}{1000 \, \text{mg}}} \]

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