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:
- Number of atoms in a grain of sand = \( 6 \times 10^{19} \)
- Number of grains in a cubic foot of sand = \( 4 \times 10^{9} \)
Now, we perform the calculation:
\[ \text{Total atoms} = (\text{Number of atoms in a grain}) \times (\text{Number of grains in a cubic foot}) \]
\[ \text{Total atoms} = (6 \times 10^{19}) \times (4 \times 10^{9}) \]
Next, we can multiply the coefficients (6 and 4) and the powers of 10 separately:
\[ = (6 \times 4) \times (10^{19} \times 10^{9}) \] \[ = 24 \times 10^{28} \]
Now, we convert \( 24 \) into scientific notation. \( 24 \) can be expressed as \( 2.4 \times 10^{1} \), so we have:
\[ 24 \times 10^{28} = (2.4 \times 10^{1}) \times 10^{28} = 2.4 \times 10^{29} \]
Thus, the total number of atoms in a cubic foot of sand is:
\[ \boxed{2.4 \times 10^{29}} \]