To find the total number of atoms in a cubic foot of sand, you can multiply the number of atoms in a grain of sand by the number of grains in a cubic foot.
Given:
- Atoms in a grain of sand = \( 6 \times 10^{19} \)
- Grains in a cubic foot of sand = \( 4 \times 10^{9} \)
Now, let's calculate the total number of atoms in a cubic foot of sand:
\[ \text{Total atoms} = (\text{Atoms in one grain}) \times (\text{Number of grains}) \] \[ \text{Total atoms} = (6 \times 10^{19}) \times (4 \times 10^{9}) \]
When multiplying the coefficients (6 and 4):
\[ 6 \times 4 = 24 \]
When multiplying the powers of 10:
\[ 10^{19} \times 10^{9} = 10^{(19 + 9)} = 10^{28} \]
Now, combine the results:
\[ \text{Total atoms} = 24 \times 10^{28} \]
So, the answer in scientific notation is:
24×10²⁸ (24 times 10 to the power of 28).