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The density of mercury is 13.6 grams per cubic centimeter. Complete the steps for converting [tex]13.6 \, g/cm^3[/tex] to [tex]kg/m^3[/tex].

[tex]\[
1 \, kg = 1,000 \, g \quad 1 \, m^3 = 10^6 \, cm^3
\][/tex]

Labels:
- 13,600
- [tex]10^6[/tex]
- 1,360
- 1 g
- 1 kg
- [tex]1 m^3[/tex]

Equation:
[tex]\[
\frac{13.6 \, g}{cm^3} \times \frac{1 \, kg}{1,000 \, g} \times \frac{10^6 \, cm^3}{1 \, m^3} = \frac{13,600 \, kg}{m^3}
\][/tex]


Sagot :

To convert the density of mercury from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³), we need to use the given conversion factors: [tex]\(1 kg = 1000 g \)[/tex] and [tex]\(1 m³ = 10^6 cm³\)[/tex].

The steps for this conversion process are as follows:

1. Start with the original density: [tex]\( \frac{13.6 \, g}{cm^3} \)[/tex].
2. Convert grams to kilograms by using the factor [tex]\( \frac{1 \, kg}{1000 \, g} \)[/tex].
3. Convert cubic centimeters to cubic meters by using the factor [tex]\( \frac{10^6 \, cm^3}{1 \, m^3} \)[/tex].

When we apply these conversion factors, the equation becomes:
[tex]\[ \frac{13.6 \, g}{cm^3} \times \frac{1 \, kg}{1000 \, g} \times \frac{10^6 \, cm^3}{1 \, m^3} = \frac{13600 \, kg}{m^3} \][/tex]

Therefore, plugging the appropriate labels into the equation, we get:
[tex]\[ \frac{13.6 \, g}{cm^3} \times \frac{1 \, kg}{1000 \, g} \times \frac{10^6 \, cm^3}{1 \, m^3} = \frac{13600 \, kg}{m^3} \][/tex]