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
2.4 times 10 superscript 28 baseline

24×1028
24 times 10 superscript 28 baseline

2.4×1029
2.4 times 10 superscript 29 baseline

24×1029

Answer 1

To find the total number of atoms in a cubic foot of sand using the given figures, we can use the following calculation:

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

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

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

Substituting the values:

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

Next, we can combine the constants and the powers of ten:

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

Now, we convert \(24 \times 10^{28}\) into proper scientific notation:

\[ 24 \times 10^{28} = 2.4 \times 10^{29} \]

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

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