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A sheet of glass has a density of

2.5(g)/(cm^(3))". "
What is the density of the glass in
(kg)/(m^(3)) ?

(kg)/(m^(3))

A sheet of glass has a density of $\frac{2.5\,\text{g}}{\text{cm}^3}$ . $\newline$ What is the density of the glass in $\frac{\text{kg}}{\text{m}^3}$ ? $\newline$ $\square$ $\frac{\text{kg}}{\text{m}^3}$

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Convert rates and measurements: customary units

Full solution

Q. A sheet of glass has a density of

\frac{2.5\,\text{g}}{\text{cm}^3}

.

\newline

What is the density of the glass in

\frac{\text{kg}}{\text{m}^3}

?

\newline

\square

\frac{\text{kg}}{\text{m}^3}

Conversion Factors: To convert the density from grams per cubic centimeter to kilograms per cubic meter, we need to know the conversion factors between these units. We know that $1$ kilogram is equal to $1000$ grams, and $1$ meter is equal to $100$ centimeters. Therefore, $1$ cubic meter is equal to $100^3$ cubic centimeters.
Setup Conversion: Using the conversion factors, we can set up the conversion as follows: $\newline$ Density in $\text{kg/m}^3$ = Density in $\text{g/cm}^3$ * $1000 \, \text{g/kg}$ * $100 \, \text{cm/m}$ ^ $3$
Plug in Density: Now we plug in the given density of the glass: $\newline$ Density in $\text{kg/m}^3$ = $2.5 \, \text{g/cm}^3$ * $1000 \, \text{g/kg}$ * $100 \, \text{cm/m}$ ^ $3$
Simplify Equation: We simplify the equation by canceling out the units and calculating the result: $\newline$ Density in $\text{kg/m}^3$ = $2.5 \times 1000 \times 100^3$ $\text{kg/m}^3$
Perform Calculation: Perform the calculation: $\newline$ Density in $\text{kg/m}^3$ = $2.5 \times 1000 \times 1000000$ $\text{kg/m}^3$ $\newline$ Density in $\text{kg/m}^3$ = $2500 \times 1000000$ $\text{kg/m}^3$ $\newline$ Density in $\text{kg/m}^3$ = $2500000000$ $\text{kg/m}^3$ $\newline$ This is incorrect because the exponent was not applied correctly to the conversion factor $(100 \text{ cm/m})^3$ . It should be $2.5 \times 1000 \times 1000000$ $0$ , not $2.5 \times 1000 \times 1000000$ $1$ .

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