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Answer :
We are given:
- The mass of a grain of sand:
[tex]$$6 \times 10^{-2}\text{ grams},$$[/tex]
- The mass of Earth:
[tex]$$6 \times 10^{28}\text{ grams}.$$[/tex]
To find how many times the mass of the grain of sand the mass of Earth is, we divide the mass of Earth by the mass of the grain of sand. That is,
[tex]$$
\text{Mass Ratio} = \frac{6 \times 10^{28}}{6 \times 10^{-2}}.
$$[/tex]
Step 1: Divide the coefficients (6 divided by 6):
[tex]$$
\frac{6}{6} = 1.
$$[/tex]
Step 2: Divide the powers of ten by subtracting exponents:
[tex]$$
10^{28} \div 10^{-2} = 10^{28 - (-2)} = 10^{28 + 2} = 10^{30}.
$$[/tex]
Thus, the mass ratio is
[tex]$$
1 \times 10^{30} = 10^{30}.
$$[/tex]
This means that the mass of Earth is [tex]$10^{30}$[/tex] times the mass of a grain of sand.
- The mass of a grain of sand:
[tex]$$6 \times 10^{-2}\text{ grams},$$[/tex]
- The mass of Earth:
[tex]$$6 \times 10^{28}\text{ grams}.$$[/tex]
To find how many times the mass of the grain of sand the mass of Earth is, we divide the mass of Earth by the mass of the grain of sand. That is,
[tex]$$
\text{Mass Ratio} = \frac{6 \times 10^{28}}{6 \times 10^{-2}}.
$$[/tex]
Step 1: Divide the coefficients (6 divided by 6):
[tex]$$
\frac{6}{6} = 1.
$$[/tex]
Step 2: Divide the powers of ten by subtracting exponents:
[tex]$$
10^{28} \div 10^{-2} = 10^{28 - (-2)} = 10^{28 + 2} = 10^{30}.
$$[/tex]
Thus, the mass ratio is
[tex]$$
1 \times 10^{30} = 10^{30}.
$$[/tex]
This means that the mass of Earth is [tex]$10^{30}$[/tex] times the mass of a grain of sand.
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