Answer :
To express the number 69,000,000,000 in scientific notation, follow these steps:
1. Identify the Significant Figures:
Start by placing a decimal after the first significant figure, which is "6" in this case. This gives us 6.9.
2. Count the Number of Places the Decimal Moves:
The original number is 69,000,000,000. When you place the decimal after the "6", you've essentially moved it 10 places to the left to transform it into 6.9.
3. Express the Number in Scientific Notation:
Scientific notation is typically in the form of [tex]\( a \times 10^n \)[/tex], where [tex]\( a \)[/tex] is a number greater than or equal to 1 and less than 10, and [tex]\( n \)[/tex] is an integer.
In this case, after moving the decimal point 10 places, the number becomes 6.9. Therefore, the scientific notation is [tex]\( 6.9 \times 10^{10} \)[/tex].
4. Choose the Correct Option:
Looking at the options given:
- [tex]\( 69 \times 10^9 \)[/tex] is incorrect because the significant figure should be between 1 and 10.
- [tex]\( 6.9^{10} \)[/tex] is not the appropriate format for scientific notation.
- [tex]\( 6.9 \times 10^{10} \)[/tex] is the correct expression based on our steps above.
Therefore, the correct answer is [tex]\( 6.9 \times 10^{10} \)[/tex].
1. Identify the Significant Figures:
Start by placing a decimal after the first significant figure, which is "6" in this case. This gives us 6.9.
2. Count the Number of Places the Decimal Moves:
The original number is 69,000,000,000. When you place the decimal after the "6", you've essentially moved it 10 places to the left to transform it into 6.9.
3. Express the Number in Scientific Notation:
Scientific notation is typically in the form of [tex]\( a \times 10^n \)[/tex], where [tex]\( a \)[/tex] is a number greater than or equal to 1 and less than 10, and [tex]\( n \)[/tex] is an integer.
In this case, after moving the decimal point 10 places, the number becomes 6.9. Therefore, the scientific notation is [tex]\( 6.9 \times 10^{10} \)[/tex].
4. Choose the Correct Option:
Looking at the options given:
- [tex]\( 69 \times 10^9 \)[/tex] is incorrect because the significant figure should be between 1 and 10.
- [tex]\( 6.9^{10} \)[/tex] is not the appropriate format for scientific notation.
- [tex]\( 6.9 \times 10^{10} \)[/tex] is the correct expression based on our steps above.
Therefore, the correct answer is [tex]\( 6.9 \times 10^{10} \)[/tex].
