a rectangular piece of iron has sides with lengths of 7.08×10⁻³ m, 2.18×10⁻² m, and 4.51×10⁻³ m. what is the…

Explanation:

Step1: Recall volume formula

The volume $V$ of a rectangular - solid is given by $V = l\times w\times h$, where $l$, $w$, and $h$ are the lengths of its sides.

Step2: Substitute the given values

We have $l = 7.08\times10^{-3}\text{ m}$, $w = 2.18\times10^{-2}\text{ m}$, and $h = 4.51\times10^{-3}\text{ m}$. Then $V=(7.08\times10^{-3})\times(2.18\times10^{-2})\times(4.51\times10^{-3})$.

Step3: Multiply the coefficients and add the exponents

First, multiply the coefficients: $7.08\times2.18\times4.51 = 7.08\times(2.18\times4.51)=7.08\times9.8218 = 69.538344$. Then, add the exponents of 10: $-3+( - 2)+(-3)=-8$. So $V = 69.538344\times10^{-8}\text{ m}^3$.

Step4: Convert to scientific - notation

Rewrite $69.538344\times10^{-8}$ in proper scientific notation. Move the decimal point one place to the left to get a number between 1 and 10, so $69.538344\times10^{-8}=6.9538344\times10^{-7}\text{ m}^3\approx6.96\times10^{-7}\text{ m}^3$.

Answer:

$6.96\times 10^{-7}\text{ m}^3$