Question

There about 6×10^19 atoms in a grain of sand. A cubic foot of sand can hold about 4×10^9 grains of sand of average size. Using those figures, how many atoms would you expect to find in a cubic foot of sand? Write the answer in scientific notation.

A. 2.4×10^29
B. 24×10^28
C. 24×10^29
D. 2.4×10^28

Answer 1

To find the number of atoms in a cubic foot of sand, we can multiply the number of grains of sand in a cubic foot by the number of atoms in a single grain of sand.

1. **Number of grains in a cubic foot of sand**: \( 4 \times 10^9 \) grains
2. **Number of atoms in a grain of sand**: \( 6 \times 10^{19} \) atoms

Now, we calculate the total number of atoms in a cubic foot of sand:

\[
\text{Total atoms} = (\text{Number of grains}) \times (\text{Number of atoms per grain})
\]
\[
= (4 \times 10^9) \times (6 \times 10^{19})
\]

Now we can multiply these values together:

\[
= 4 \times 6 \times 10^9 \times 10^{19}
\]
\[
= 24 \times 10^{28}
\]

Next, we express \( 24 \times 10^{28} \) in proper scientific notation:

\[
= 2.4 \times 10^{29}
\]

Hence, the expected number of atoms in a cubic foot of sand is \( 2.4 \times 10^{29} \).

The correct answer is **A. \( 2.4 \times 10^{29} \)**.