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Complete the [tex]$kg[tex]$[/tex] to [tex]$[/tex]mL$[/tex] roadmap.

Select the correct conversion factor for each step in the following roadmap for a substance with a density of [tex]$1 \, g/mL$[/tex]:

[tex]\[
\begin{array}{l}
\times \frac{1 \, mL }{1000 \, L } \times \frac{1000 \, g }{1 \, kg } \\
\times \frac{1 \, g }{1 \, mL } \times \frac{1000 \, L }{1 \, mL } \\
\times \frac{1010 \, kg }{1 \, n } \times \frac{1 \, mL }{1 \, g } \\
\times \frac{1 \, g }{10011 \, mL }
\end{array}
\][/tex]

mass (kg) → mass (g)



Answer :

GinnyAnswer
First, let's review what we need to do: we want to convert from kilograms (kg) to milliliters (mL). Given the density of the substance is \(1 \text{ g/mL}\), which means \(1 \text{ gram}\) of the substance occupies \(1 \text{ milliliter}\).

### Step-by-Step Roadmap for Converting kg to mL

1. Convert kilograms (kg) to grams (g):
- Since \(1 \text{ kg}\) is equal to \(1000 \text{ grams}\), the conversion factor is:
[tex]\[\frac{1000 \text{ grams}}{1 \text{ kg}}\][/tex]

2. Convert grams (g) to milliliters (mL) (using the density):
- The density tells us that \(1 \text{ gram} \) is equivalent to \(1 \text{ mL}\). Therefore, the conversion factor is:
[tex]\[\frac{1 \text{ mL}}{1 \text{ gram}}\][/tex]

### Now let's combine the conversion factors:

1. Starting from kilograms (kg), convert to grams (g):
[tex]\[ \text{mass (kg)} \times \frac{1000 \text{ g}}{1 \text{ kg}} \][/tex]

2. Then convert grams (g) to milliliters (mL) using the density information:
[tex]\[ \text{mass (g)} \times \frac{1 \text{ mL}}{1 \text{ g}} \][/tex]

Therefore, the complete step-by-step roadmap for converting some mass in kilograms (kg) to milliliters (mL) for a substance with a density of 1 g/mL is:

[tex]\[ \text{mass (kg)} \times \frac{1000 \text{ g}}{1 \text{ kg}} \times \frac{1 \text{ mL}}{1 \text{ g}} \][/tex]

By multiplying these factors together, extraneous conversion factors like \( \times \frac{1 mL }{1000 L } \times \frac{1000 L }{1 mL }\) and incorrect conversions such as \( \times \frac{1010 kg }{1 n } \times \frac{1 mL }{1 g } \times \frac{1 g }{10011 mL } \) do not contribute to the accurate roadmap. The correct conversion factors should be:

[tex]\[ \left(0.001,\ 1000,\ 1,\ 1000 \right) \][/tex]

where:
- \(0.001\) represents the fraction when converting milliliters to liters inadvertently coming out to 0.001 grams per milliliter (not directly relevant in conversion for \(kg\) to \(mL\))
- \(1000\) represents conversion from kg to grams,
- \(1\) reflects density hence converting grams to milliliters directly
- \(1000\) provides inverse completeness of system checking albeit least used only for scaling reasons

The final conversion factors for each correct step summing to combine \(kg\) to \(mL\) are:

1. \(\frac{1000 \text{ grams}}{1 \text{ kg}}\)
2. \(\frac{1 \text{ mL}}{1 \text{ gram}}\)

I hope this helps! Feel free to ask more questions if you have any.

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