an atom of gold has a mass of approximately 3.25×10⁻²² grams. what is the mass of 7000 atoms of gold…

Explanation:

Step1: Write the multiplication expression

We need to multiply the mass of one - gold atom by the number of atoms. The mass of one gold atom is $3.25\times 10^{-22}$ grams and the number of atoms is 7000. We can write 7000 as $7\times10^{3}$. So the expression is $(3.25\times 10^{-22})\times(7\times 10^{3})$.

Step2: Use the commutative and associative properties of multiplication

$(3.25\times 7)\times(10^{-22}\times 10^{3})$.

Step3: Calculate the product of the non - exponential parts and the exponential parts separately

$3.25\times7 = 22.75$, and using the rule $a^{m}\times a^{n}=a^{m + n}$, we have $10^{-22}\times 10^{3}=10^{-22 + 3}=10^{-19}$. So the result is $22.75\times 10^{-19}$.

Step4: Convert to proper scientific notation

In scientific notation, the coefficient should be between 1 and 10. We rewrite $22.75\times 10^{-19}$ as $2.275\times 10^{-18}$ (since $22.75 = 2.275\times10^{1}$ and $2.275\times10^{1}\times10^{-19}=2.275\times10^{-18}$).

Answer:

$2.275\times 10^{-18}$ grams