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Answer :
To solve the problem of finding the mass of a grain of sand, we start with the given scientific notation for the mass:
The mass of a grain of sand is approximately [tex]\( 2.8 \times 10^{-11} \)[/tex] grams.
When expressing this number in standard notation (a decimal number), we need to understand the concept of scientific notation. The number [tex]\( 2.8 \times 10^{-11} \)[/tex] means that we start with 2.8 and move the decimal point 11 places to the left.
Here is a step-by-step breakdown:
1. Start by writing 2.8 as a regular decimal: 2.8.
2. Move the decimal point 11 places to the left. Since 2.8 only has one digit to the left of the decimal point, we add leading zeros to accommodate the full 11 places shift:
[tex]\[
0.000000000028
\][/tex]
In standard form, this number is written as:
[tex]\[
2.8 \times 10^{-11} = 0.000000000028
\][/tex]
Given the final computation and result:
The mass of a grain of sand, when converted from scientific notation [tex]\( 2.8 \times 10^{-11} \)[/tex] to standard form, yields:
[tex]\[
0.000000000028
\][/tex]
Thus, the numerical value of the mass of a grain of sand in standard form is approximately:
[tex]\[
2.7999999999999997 \times 10^{-11}
\][/tex]
which is effectively the same as:
[tex]\[
0.000000000028
\][/tex]
The mass of a grain of sand is approximately [tex]\( 2.8 \times 10^{-11} \)[/tex] grams.
When expressing this number in standard notation (a decimal number), we need to understand the concept of scientific notation. The number [tex]\( 2.8 \times 10^{-11} \)[/tex] means that we start with 2.8 and move the decimal point 11 places to the left.
Here is a step-by-step breakdown:
1. Start by writing 2.8 as a regular decimal: 2.8.
2. Move the decimal point 11 places to the left. Since 2.8 only has one digit to the left of the decimal point, we add leading zeros to accommodate the full 11 places shift:
[tex]\[
0.000000000028
\][/tex]
In standard form, this number is written as:
[tex]\[
2.8 \times 10^{-11} = 0.000000000028
\][/tex]
Given the final computation and result:
The mass of a grain of sand, when converted from scientific notation [tex]\( 2.8 \times 10^{-11} \)[/tex] to standard form, yields:
[tex]\[
0.000000000028
\][/tex]
Thus, the numerical value of the mass of a grain of sand in standard form is approximately:
[tex]\[
2.7999999999999997 \times 10^{-11}
\][/tex]
which is effectively the same as:
[tex]\[
0.000000000028
\][/tex]
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