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Interconverting Compound SI Units: ALEKS Answer

The conversion is 4.5 mol/(g·cm²). Convert kilograms to grams and square the meter-to-centimeter factor so every denominator unit cancels correctly.

Question

Interconverting compound SI unitsConvert the following measurement:4.5 × 10^7 mol/(kg·m²) = ? mol/(g·cm²)

Answer

4.5 mol/(g⋅cm2)\boxed{4.5\ \mathrm{mol/(g\cdot cm^2)}}

Convert each denominator unit with a factor arranged to cancel the original unit:

4.5×107 molkg⋅m2×1 kg1000 g×(1 m100 cm)2.4.5\times10^7\ \frac{\mathrm{mol}}{\mathrm{kg\cdot m^2}} \times\frac{1\ \mathrm{kg}}{1000\ \mathrm{g}} \times\left(\frac{1\ \mathrm{m}}{100\ \mathrm{cm}}\right)^2.

The mass conversion contributes 10−310^{-3}. Because the length unit is squared, the area conversion contributes (10−2)2=10−4(10^{-2})^2=10^{-4}. Together they contribute 10−710^{-7}:

4.5×107×10−7=4.5.4.5\times10^7\times10^{-7}=4.5.

The squared length unit is the key: converting m2\mathrm{m^2} to cm2\mathrm{cm^2} requires squaring the entire meter-to-centimeter factor, not just changing the unit label.

Evidence boundary

This answer solves the exact 4.5 × 10^7 mol/(kg·m²) version shown in the cited question source. It uses exact SI prefix relationships and applies the meter-to-centimeter factor twice because the length unit is squared; no experimental data or alternate ALEKS values are assumed.

Sources

These references support the concepts and methods used in the explanation above.

Interconverting Compound SI Units ALEKS Answer | Verla