Question

There are about 6×1019
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

24×1029
24 times 10 superscript 29 baseline

2.4×1029
2.4 times 10 superscript 29 baseline

24×1028

Answer 1

To find the total number of atoms in a cubic foot of sand, you need to multiply the number of grains of sand in a cubic foot by the number of atoms in each grain of sand.

Given:
- Number of atoms in a grain of sand = \(6 \times 10^{19}\)
- Number of grains of sand in a cubic foot = \(4 \times 10^{9}\)

So, the total number of atoms in a cubic foot of sand can be calculated as:

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

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

Now, performing the multiplication:

1. Multiply the coefficients: \(6 \times 4 = 24\)
2. Add the exponents (since we are multiplying powers of 10): \(10^{19} \times 10^{9} = 10^{28}\)

Putting it all together, we get:
\[
\text{Total atoms} = 24 \times 10^{28}
\]

To express this in proper scientific notation, we should write it as:
\[
2.4 \times 10^{29}
\]

Thus, the correct response is:
**2.4×10²⁹**.