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QuestionSimplify the unit: 9.2g⋅cm3g⋅cm29.2 \frac{\mathrm{g} \cdot \mathrm{cm}^{3}}{\mathrm{g} \cdot \mathrm{cm}^{2}}. What is the simplest form?

Studdy Solution

STEP 1

Assumptions1. The given measurement is 9.g⋅cm3 g⋅cm9. \frac{\mathrm{g} \cdot \mathrm{cm}^{3}}{\mathrm{~g} \cdot \mathrm{cm}^{}} . We need to simplify the unit if possible

STEP 2

First, we need to understand the unit of the given measurement. It's a ratio of mass times volume (grams times cubic centimeters) to mass times area (grams times square centimeters).

STEP 3

To simplify the unit, we can cancel out the common terms in the numerator and the denominator.

STEP 4

The grams (g) in the numerator and denominator cancel out.
9.2g⋅cm3 g⋅cm2=9.2cm3cm29.2 \frac{\mathrm{g} \cdot \mathrm{cm}^{3}}{\mathrm{~g} \cdot \mathrm{cm}^{2}} =9.2 \frac{\mathrm{cm}^{3}}{\mathrm{cm}^{2}}

STEP 5

Next, we can simplify the cubic centimeters (cm^3) and square centimeters (cm^2) by subtracting the exponent in the denominator from the exponent in the numerator.

STEP 6

The cubic centimeters (cm^3) and square centimeters (cm^2) simplify to centimeters (cm).
9.2cm3cm2=9.2cm9.2 \frac{\mathrm{cm}^{3}}{\mathrm{cm}^{2}} =9.2 \mathrm{cm}The simplified unit for the given measurement is cm (centimeters).

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