Answer :
Certainly! Let's solve the problem step-by-step and find out how many grains of sand are in 10 kilograms of sand.
1. Understand the Problem:
- We know the mass of a single grain of sand is about [tex]\(10^{-3}\)[/tex] grams.
- We want to determine how many grains of this sand are in 10 kilograms.
2. Convert Units:
- Since the mass of each grain is given in grams, and we have the mass of the sand in kilograms, we need to convert the kilograms into grams.
- 1 kilogram is equal to 1000 grams. Therefore, 10 kilograms is:
[tex]\[
10 \, \text{kg} \times 1000 \, \frac{\text{grams}}{\text{kg}} = 10,000 \, \text{grams}
\][/tex]
3. Calculate the Number of Grains:
- Now, you can find out how many grains fit into the total mass by dividing the total mass of the sand by the mass of one grain.
- Total mass of sand (in grams) = 10,000 grams.
- Mass of one grain of sand = [tex]\(0.001\)[/tex] grams.
- The number of grains is calculated as follows:
[tex]\[
\frac{\text{Total mass of sand}}{\text{Mass of one grain}} = \frac{10,000 \, \text{grams}}{0.001 \, \text{grams/grain}}
\][/tex]
4. Solve the Calculation:
- Perform the division to find the number of grains:
[tex]\[
\frac{10,000}{0.001} = 10,000,000
\][/tex]
So, there are about 10,000,000 grains of sand in 10 kilograms of sand.
1. Understand the Problem:
- We know the mass of a single grain of sand is about [tex]\(10^{-3}\)[/tex] grams.
- We want to determine how many grains of this sand are in 10 kilograms.
2. Convert Units:
- Since the mass of each grain is given in grams, and we have the mass of the sand in kilograms, we need to convert the kilograms into grams.
- 1 kilogram is equal to 1000 grams. Therefore, 10 kilograms is:
[tex]\[
10 \, \text{kg} \times 1000 \, \frac{\text{grams}}{\text{kg}} = 10,000 \, \text{grams}
\][/tex]
3. Calculate the Number of Grains:
- Now, you can find out how many grains fit into the total mass by dividing the total mass of the sand by the mass of one grain.
- Total mass of sand (in grams) = 10,000 grams.
- Mass of one grain of sand = [tex]\(0.001\)[/tex] grams.
- The number of grains is calculated as follows:
[tex]\[
\frac{\text{Total mass of sand}}{\text{Mass of one grain}} = \frac{10,000 \, \text{grams}}{0.001 \, \text{grams/grain}}
\][/tex]
4. Solve the Calculation:
- Perform the division to find the number of grains:
[tex]\[
\frac{10,000}{0.001} = 10,000,000
\][/tex]
So, there are about 10,000,000 grains of sand in 10 kilograms of sand.
