There are about 6×1019%0D%0A6%0D%0A×%0D%0A10%0D%0A19%0D%0A atoms in a grain of sand. A cubic foot of sand can hold about 4×109%0D%0A4%0D%0A×%0D%0A10%0D%0A9%0D%0A 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)%0D%0AResponses%0D%0A%0D%0A2.4×1028%0D%0A2.4%0D%0A×%0D%0A10%0D%0A28%0D%0A2 point 4 times 10 to the 28th power%0D%0A%0D%0A2.4×1029%0D%0A2.4%0D%0A×%0D%0A10%0D%0A29%0D%0A2 point 4 times 10 to the 29th power%0D%0A%0D%0A24×1028%0D%0A24%0D%0A×%0D%0A10%0D%0A28%0D%0A24 times 10 to the 28th power%0D%0A%0D%0A24×1029%0D%0A24%0D%0A×%0D%0A10%0D%0A29

Answer 1

To find the number of atoms in a cubic foot of sand, you can multiply the number of grains of sand in a cubic foot by the number of atoms in a grain of sand.

1. The number of atoms in a grain of sand is given as \(6 \times 10^{19}\).
2. The number of grains in a cubic foot of sand is given as \(4 \times 10^9\).

Now, multiply these two values:

\[ (6 \times 10^{19}) \times (4 \times 10^9) \]

You can multiply the coefficients (the numbers in front) and the powers of ten separately:

\[ 6 \times 4 = 24 \]

For the powers of ten:

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

Now, combine the results:

\[ 24 \times 10^{28} \]

In scientific notation, this can be written as:

\[ 2.4 \times 10^{29} \quad \text{(because } 24 = 2.4 \times 10^1\text{)} \]

Thus, in scientific notation, the number of atoms you would expect to find in a cubic foot of sand is:

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

Answer 2

u sure

Answer 3

Let’s carefully verify the calculations.

1. We have the number of atoms in a grain of sand: \[ 6 \times 10^{19} , \text{atoms per grain} \]

2. We also have the number of grains of sand in a cubic foot: \[ 4 \times 10^{9} , \text{grains per cubic foot} \]

Now, to find the total number of atoms in a cubic foot of sand, we need to multiply these two quantities:

\[ (6 \times 10^{19}) \times (4 \times 10^{9}) \]

Step 1: Multiply the coefficients: \[ 6 \times 4 = 24 \]

Step 2: Multiply the powers of ten: \[ 10^{19} \times 10^{9} = 10^{19 + 9} = 10^{28} \]

Step 3: Combine both results: \[ 24 \times 10^{28} \]

Step 4: Convert to proper scientific notation: To express \(24\) in scientific notation: \[ 24 = 2.4 \times 10^{1} \]

Thus we multiply: \[ 24 \times 10^{28} = (2.4 \times 10^{1}) \times 10^{28} = 2.4 \times 10^{29} \]

So the final result, the expected number of atoms in a cubic foot of sand, is: \[ \boxed{2.4 \times 10^{29}} \]

Yes, I am confident that the correct answer is indeed \(2.4 \times 10^{29}\). Thank you for your patience!