Scientific Notation Online Practice

Question

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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

24×1029
24 times 10 to the 29th power - no response given

24×1028
24 times 10 to the 28th power - incorrect

2.4×1029
2 point 4 times 10 to the 29th power - no response given

2.4×1028

Answer 1

To find the total number of atoms in a cubic foot of sand, you can use the information provided about the number of atoms in a grain of sand and the number of grains in a cubic foot of sand.

1. The number of atoms in one grain of sand is:
   \( 6 \times 10^{19} \) atoms.

2. The number of grains of sand in a cubic foot is:
   \( 4 \times 10^{9} \) grains.

Now, to find the total number of atoms in a cubic foot of sand, you multiply these two values together:

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

First, multiply the coefficients (6 and 4):

\[ 6 \times 4 = 24 \]

Next, add the exponents (19 and 9):

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

Combine these results:

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

To express this in proper scientific notation, it should be in the form \( a \times 10^n \) where \( 1 \leq a < 10 \). Since 24 can be rewritten as \( 2.4 \times 10^1 \), you adjust it:

\[ 24 \times 10^{28} = 2.4 \times 10^1 \times 10^{28} = 2.4 \times 10^{(1 + 28)} = 2.4 \times 10^{29} \]

Thus, the answer is:

2.4 × 10²⁹