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Answer :
To find the total mass of sand on the beach, we need to calculate the product of the mass of a single grain of sand and the total number of grains on the beach. Here’s how you can do it:
1. Understand the values given:
- Each grain of sand has a mass of approximately [tex]\(2.3 \times 10^{-4}\)[/tex] grams.
- The beach contains about [tex]\(45 \times 10^{12}\)[/tex] grains of sand.
2. Multiply the mass of one grain by the total number of grains:
[tex]\[
\text{Total mass} = (2.3 \times 10^{-4}) \times (45 \times 10^{12})
\][/tex]
3. Combine the numerical parts and the powers of ten separately:
- First, multiply the numerical parts: [tex]\(2.3 \times 45 = 103.5\)[/tex]
- Next, multiply the powers of ten: [tex]\(10^{-4} \times 10^{12} = 10^{8}\)[/tex]
4. Combine the results:
[tex]\[
\text{Total mass} = 103.5 \times 10^{8}
\][/tex]
5. Express the result in scientific notation:
- Adjust 103.5 to proper scientific notation: [tex]\(1.035 \times 10^2\)[/tex]
- Finally, combine: [tex]\(1.035 \times 10^2 \times 10^8 = 1.035 \times 10^{10}\)[/tex]
Therefore, the total mass of the sand on the beach is [tex]\(1.035 \times 10^{10}\)[/tex] grams.
1. Understand the values given:
- Each grain of sand has a mass of approximately [tex]\(2.3 \times 10^{-4}\)[/tex] grams.
- The beach contains about [tex]\(45 \times 10^{12}\)[/tex] grains of sand.
2. Multiply the mass of one grain by the total number of grains:
[tex]\[
\text{Total mass} = (2.3 \times 10^{-4}) \times (45 \times 10^{12})
\][/tex]
3. Combine the numerical parts and the powers of ten separately:
- First, multiply the numerical parts: [tex]\(2.3 \times 45 = 103.5\)[/tex]
- Next, multiply the powers of ten: [tex]\(10^{-4} \times 10^{12} = 10^{8}\)[/tex]
4. Combine the results:
[tex]\[
\text{Total mass} = 103.5 \times 10^{8}
\][/tex]
5. Express the result in scientific notation:
- Adjust 103.5 to proper scientific notation: [tex]\(1.035 \times 10^2\)[/tex]
- Finally, combine: [tex]\(1.035 \times 10^2 \times 10^8 = 1.035 \times 10^{10}\)[/tex]
Therefore, the total mass of the sand on the beach is [tex]\(1.035 \times 10^{10}\)[/tex] grams.
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