Answer :
Sure, let's solve the problem step-by-step.
We are given the mass of Earth as [tex]\( 5,970,000,000,000,000,000,000,000 \)[/tex] kg. We need to express this number in scientific notation.
1. Identify the significant figures:
The significant figures are the digits that convey the actual magnitude of the number without the place-holding zeros. Here, the significant figures are `597`.
2. Determine the correct placement for the decimal point:
Scientific notation requires that the number be written as a decimal between 1 and 10. Thus, we need to place the decimal point after the first digit:
[tex]\[ 5.97 \][/tex]
3. Count the number of places the decimal point has moved:
Starting from the original number, the decimal point moves from the end of the number to just after the first digit `5`. Let's count the places:
[tex]\[ 5,970,000,000,000,000,000,000,000 \rightarrow 5.970 \times 10^{24} \][/tex]
This means the decimal point moves 24 places to the left.
4. Write the number in scientific notation:
Combining the significant figures with the exponent, the number is expressed as [tex]\( 5.97 \times 10^{24} \)[/tex].
5. Verify the options:
Comparing our result with the provided options:
- A. [tex]\( 5.97 \times 10^{24} \)[/tex] kg
- B. [tex]\( 59.7 \times 10^{23} \)[/tex] kg
- C. [tex]\( 5.97^{24} \)[/tex] kg
- D. [tex]\( 5.97 \times 10^{22} \)[/tex] kg
Option A matches our result.
Therefore, scientists would express Earth's mass as:
[tex]\[ \boxed{5.97 \times 10^{24} \text{ kg}} \][/tex]
Option A is the correct answer.
We are given the mass of Earth as [tex]\( 5,970,000,000,000,000,000,000,000 \)[/tex] kg. We need to express this number in scientific notation.
1. Identify the significant figures:
The significant figures are the digits that convey the actual magnitude of the number without the place-holding zeros. Here, the significant figures are `597`.
2. Determine the correct placement for the decimal point:
Scientific notation requires that the number be written as a decimal between 1 and 10. Thus, we need to place the decimal point after the first digit:
[tex]\[ 5.97 \][/tex]
3. Count the number of places the decimal point has moved:
Starting from the original number, the decimal point moves from the end of the number to just after the first digit `5`. Let's count the places:
[tex]\[ 5,970,000,000,000,000,000,000,000 \rightarrow 5.970 \times 10^{24} \][/tex]
This means the decimal point moves 24 places to the left.
4. Write the number in scientific notation:
Combining the significant figures with the exponent, the number is expressed as [tex]\( 5.97 \times 10^{24} \)[/tex].
5. Verify the options:
Comparing our result with the provided options:
- A. [tex]\( 5.97 \times 10^{24} \)[/tex] kg
- B. [tex]\( 59.7 \times 10^{23} \)[/tex] kg
- C. [tex]\( 5.97^{24} \)[/tex] kg
- D. [tex]\( 5.97 \times 10^{22} \)[/tex] kg
Option A matches our result.
Therefore, scientists would express Earth's mass as:
[tex]\[ \boxed{5.97 \times 10^{24} \text{ kg}} \][/tex]
Option A is the correct answer.
