There are about 6×1019

Question

atoms in a grain of sand. A cubic foot of sand can hold about 4×109
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.(1 point)
Responses

2.4×1028
2 point 4 times 10 to the 28th power

2.4×1029
2 point 4 times 10 to the 29th power

24×1028
24 times 10 to the 28th power

24×1029

Answer 1

To determine the number of atoms in a cubic foot of sand, we can use the given data:

1. There are about \( 6 \times 10^{19} \) atoms in a grain of sand.
2. A cubic foot of sand can hold about \( 4 \times 10^{9} \) grains of sand.

Now, we can calculate the total number of atoms in a cubic foot of sand using the following formula:

\[ \text{Total atoms} = (\text{Number of grains}) \times (\text{Atoms per grain}) \]

Substituting the values:

\[ \text{Total atoms} = (4 \times 10^{9}) \times (6 \times 10^{19}) \]

Next, we multiply these two terms:

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

To express this in standard scientific notation, we can rewrite \( 24 \times 10^{28} \) as:

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

Therefore, the expected number of atoms in a cubic foot of sand is

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