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Answer :
To find the total mass of the sand on the beach, we can follow these simple steps:
1. Understand the Problem:
We have a grain of sand with a mass of approximately [tex]\(2.3 \times 10^{14}\)[/tex] grams. The beach contains about [tex]\(4.5 \times 10^{12}\)[/tex] grains of sand. We need to find the total mass of all these grains combined.
2. Multiply the Values:
We multiply the mass of one grain of sand by the total number of grains to get the total mass:
[tex]\[
(2.3 \times 10^{14} \text{ grams per grain}) \times (4.5 \times 10^{12} \text{ grains})
\][/tex]
3. Perform the Multiplication Using Scientific Notation:
To multiply numbers in scientific notation, multiply the coefficients (the numbers in front) and then add the exponents.
- Coefficients: [tex]\(2.3 \times 4.5 = 10.35\)[/tex]
- Exponents: Add the exponents [tex]\(14 + 12 = 26\)[/tex].
4. Combine to Get the Answer:
The result of the multiplication is:
[tex]\[
10.35 \times 10^{26}
\][/tex]
5. Adjust to Proper Scientific Notation:
We write the result as [tex]\(1.035 \times 10^{27}\)[/tex] to ensure the coefficient is between 1 and 10.
So, the total mass of the sand on the beach is approximately [tex]\(1.035 \times 10^{27}\)[/tex] grams.
1. Understand the Problem:
We have a grain of sand with a mass of approximately [tex]\(2.3 \times 10^{14}\)[/tex] grams. The beach contains about [tex]\(4.5 \times 10^{12}\)[/tex] grains of sand. We need to find the total mass of all these grains combined.
2. Multiply the Values:
We multiply the mass of one grain of sand by the total number of grains to get the total mass:
[tex]\[
(2.3 \times 10^{14} \text{ grams per grain}) \times (4.5 \times 10^{12} \text{ grains})
\][/tex]
3. Perform the Multiplication Using Scientific Notation:
To multiply numbers in scientific notation, multiply the coefficients (the numbers in front) and then add the exponents.
- Coefficients: [tex]\(2.3 \times 4.5 = 10.35\)[/tex]
- Exponents: Add the exponents [tex]\(14 + 12 = 26\)[/tex].
4. Combine to Get the Answer:
The result of the multiplication is:
[tex]\[
10.35 \times 10^{26}
\][/tex]
5. Adjust to Proper Scientific Notation:
We write the result as [tex]\(1.035 \times 10^{27}\)[/tex] to ensure the coefficient is between 1 and 10.
So, the total mass of the sand on the beach is approximately [tex]\(1.035 \times 10^{27}\)[/tex] grams.
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