round off the answer using significant figures (2.2222 x 10^3 mm)(2.00 x 10^3 mm) = what are the units in…

Explanation:

Step1: Multiply the numbers

When multiplying numbers in scientific - notation, we multiply the coefficients and add the exponents of 10. The coefficients are 2.2222 and 2.00. Multiply the coefficients: $2.2222\times2.00 = 4.4444$. Add the exponents of 10: $10^{3}\times10^{3}=10^{3 + 3}=10^{6}$. So the result before rounding is $4.4444\times10^{6}\text{ mm}\times\text{mm}$.

Step2: Determine significant figures

The number 2.2222 has 5 significant figures and 2.00 has 3 significant figures. When multiplying, the result should be rounded to the least number of significant figures among the factors, which is 3 significant figures. Rounding $4.4444\times10^{6}$ to 3 significant figures gives $4.44\times10^{6}$.

Step3: Determine the units

When multiplying two quantities with the same unit (mm in this case), the unit of the product is the square of the original unit. So the unit is $\text{mm}^{2}$.

Answer:

mm$^{2}$