decide whether each proposed multiplication or division of measurements is possible. if it is possible…

decide whether each proposed multiplication or division of measurements is possible. if it is possible, write the result in the \nproposed multiplication or division is this possible? result\n$\frac{27. g}{9.0 cm}=?$ yes no\n$(1.2 cm^{2})cdot(0.23 m)=?$ yes no\n$(4.0 m^{3})cdot(7.0 m)=?$ yes no
Answer
Explanation:
Step1: Analyze $\frac{27\text{ g}}{9.0\text{ cm}}$
Mass divided by length is a valid operation in terms of getting a quantity with units of mass - per - length. Calculate $\frac{27}{9.0}=3$. So the result is $3\text{ g/cm}$.
Step2: Analyze $(1.2\text{ cm}^2)\cdot(0.23\text{ m})$
First, convert the units to be consistent. Since $1\text{ m} = 100\text{ cm}$, then $0.23\text{ m}=23\text{ cm}$. Then $(1.2\text{ cm}^2)\cdot(23\text{ cm})=(1.2\times23)\text{ cm}^3 = 27.6\text{ cm}^3$.
Step3: Analyze $(4.0\text{ m}^3)\cdot(7.0\text{ m})$
Volume times length gives a quantity with units of volume - times - length. Calculate $(4.0\times7.0)\text{ m}^4=28\text{ m}^4$.
Answer:
| proposed multiplication or division | Is this possible? | result |
|---|---|---|
| $\frac{27\text{ g}}{9.0\text{ cm}}$ | yes | $3\text{ g/cm}$ |
| $(1.2\text{ cm}^2)\cdot(0.23\text{ m})$ | yes | $27.6\text{ cm}^3$ |
| $(4.0\text{ m}^3)\cdot(7.0\text{ m})$ | yes | $28\text{ m}^4$ |