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 2.4×1029 2 point 4 times 10 to the 29th power 2.4×1028 2 point 4 times 10 to the 28th power 24×1029 24 times 10 to the 29th power 24×1028 24 times 10 to the 28th power

Answer 1

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

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.

We need to multiply the number of grains in a cubic foot by the number of atoms per grain:

\[ \text{Number of atoms in a cubic foot} = (4 \times 10^{9} \text{ grains}) \times (6 \times 10^{19} \text{ atoms/grain}) \]

Now, let's perform the multiplication:

\[ 4 \times 6 = 24 \]

For the powers of ten, we add the exponents:

\[ 10^{9} \times 10^{19} = 10^{(9 + 19)} = 10^{28} \]

Putting it all together, we get:

\[ \text{Number of atoms in a cubic foot} = 24 \times 10^{28} \]

Now we need to express this in proper scientific notation, which is typically represented as \( a \times 10^{n} \) where \( 1 \leq a < 10 \).

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

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

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

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