Question

One grain of sand approximately weighs 7 * 10^{-5} g. How many grains of sand are there in 6300 kg of sand? Give your answer in standard form.

Answer 1

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;

`(1)/(7* 10^(-5))= (x)/(6300000)`

`(10^5)/(7) = (x)/(6300000)`

By cross multiply we get;

`6300000 * 10^5 = 7x`

or

`63 * 10^5 * 10^5 = 7x`

`63 * 10^(5+5) = 7x` [using
`x^a \cdot x^b = x^(a+b)`]

`63 * 10^(10) = 7x`

Divide both sides by 7 we get;

`x = (63 * 10^(10))/(7) = 9 * 10^(10)`

Standard form is a way of of writing down very large or very small numbers easily.

Therefore,
`9 * 10^(10)` grains of sand are there in 6300 kg of sand.