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

24×1029
24 times 10 superscript 29 baseline

2.4×1029
2.4 times 10 superscript 29 baseline

2.4×1028
2.4 times 10 superscript 28 baseline

24×1028

Answer 1

To calculate the number of atoms in a cubic foot of sand, we can follow these steps:

1. Calculate the total number of atoms in sand by multiplying the number of grains of sand by the number of atoms per grain.

   We know:

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

   Therefore, the total number of atoms in a cubic foot of sand is: \[ \text{Total atoms} = (4 \times 10^{9}) \times (6 \times 10^{19}) \]

2. Multiply these values: \[ = 4 \times 6 \times 10^{9} \times 10^{19} \] \[ = 24 \times 10^{9 + 19} \] \[ = 24 \times 10^{28} \]

3. Convert this to proper scientific notation, which would typically have the leading digit as a number between 1 and 10: \[ = 2.4 \times 10^{29} \]

So the number of atoms you would expect to find in a cubic foot of sand is \( 2.4 \times 10^{29} \).

The correct response is: 2.4×10²⁹.