Let's go through the steps to determine how many grains of sand there are in 6300 kilograms of sand.
1. Convert the total weight from kilograms to grams:
We start by converting the total weight of sand from kilograms to grams. We know that:
[tex]\[
1 \text{ kilogram (kg)} = 1000 \text{ grams (g)}
\][/tex]
So,
[tex]\[
6300 \text{ kg} \times 1000 = 6300000 \text{ g}
\][/tex]
Therefore, 6300 kg of sand is equivalent to 6300000 grams of sand.
2. Determine the weight of a single grain of sand:
According to the provided information, the weight of one grain of sand is:
[tex]\[
7 \times 10^{-5} \text{ grams}
\][/tex]
3. Calculate the number of grains:
To find the number of grains in 6300000 grams of sand, we need to divide the total weight by the weight of one grain of sand:
[tex]\[
\frac{6300000 \text{ g}}{7 \times 10^{-5} \text{ g/grain}}
\][/tex]
4. Perform the division:
[tex]\[
\frac{6300000}{7 \times 10^{-5}}
\][/tex]
Dividing 6300000 by [tex]\(7 \times 10^{-5}\)[/tex] gives us:
[tex]\[
6300000 \times \frac{1}{7 \times 10^{-5}} = 6300000 \times \frac{1}{7} \times 10^5
\][/tex]
5. Simplify the expression:
[tex]\[
6300000 \div 7 = 900000
\][/tex]
Continuing our calculation:
[tex]\[
900000 \times 10^5 = 9 \times 10^5 \times 10^5 = 9 \times 10^{10}
\][/tex]
Therefore, the number of grains of sand in 6300 kilograms of sand is approximately [tex]\(9 \times 10^{10}\)[/tex].
This matches with the numerical answer from the provided result, which is about [tex]\(8.999999999 \times 10^{10}\)[/tex]. For the sake of clarity and standard form, we round this to:
[tex]\[
9 \times 10^{10} \text{ grains}
\][/tex]
