Answer:
Proportion states that the two ratio or fractions are equal.
Given the statement: One grain of sand approximately weighs 7 * 10^{-5} g.
To find how many grains of sand are there in 6300 kg of sand.
Let x be the number of grains of sand in 6300 kg of sand.
Using conversion :
1 kg = 1000 g
6300 kg = 6300000 g
Then, by using proportion method, we have;
[tex]\frac{1}{7\times 10^{-5}}= \frac{x}{6300000}[/tex]
[tex]\frac{10^5}{7} = \frac{x}{6300000}[/tex]
By cross multiply we get;
[tex]6300000 \times 10^5 = 7x[/tex]
or
[tex]63 \times 10^5 \times 10^5 = 7x[/tex]
[tex]63 \times 10^{5+5} = 7x[/tex] [using [tex]x^a \cdot x^b = x^{a+b}[/tex]]
[tex]63 \times 10^{10} = 7x[/tex]
Divide both sides by 7 we get;
[tex]x = \frac{63 \times 10^{10}}{7} = 9 \times 10^{10}[/tex]
Standard form is a way of of writing down very large or very small numbers easily.
Therefore, [tex]9 \times 10^{10}[/tex] grains of sand are there in 6300 kg of sand.
