Taking into account the change of units,
Rule of three
In first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
The direct rule of three is the rule applied in this case where there is a change of units.
Change of units
To perform in this case the conversion of units, you must first know that 1 m³ = 1×10²⁷ nm³. So, if 1×10²⁷ nm³ is 1 m³ , how many nm³ equals 7.8×10⁻³¹ m³?
1 m³ ⇒ 1×10²⁷ nm³
7.8×10⁻³¹ m³ ⇒ x
So: [tex]x=\frac{7.8x10^{-31} m^{3}x 1x10^{27} nm^{3}}{1m^{3}}[/tex]
Solving:
x= 7.8×10⁻⁴ nm³
In summary, the atom of a particular element has a volume of 7.8×10⁻⁴ nm³.
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