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Answer :
To express the number [tex]\( 69,000,000,000 \)[/tex] in scientific notation with the proper number of significant figures, follow these steps:
1. Identify the Significant Figures: In the original number [tex]\( 69,000,000,000 \)[/tex], there are two significant figures: '6' and '9'.
2. Form the Scientific Notation: Scientific notation is a way of expressing numbers that are too big or too small in a more compact form, typically using the format:
[tex]\[
a \times 10^n
\][/tex]
where [tex]\( a \)[/tex] is a number such that [tex]\( 1 \leqslant a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer.
3. Convert the Number: Move the decimal point such that there is only one non-zero digit to the left of the decimal point. For the number [tex]\( 69,000,000,000 \)[/tex]:
- Starting from 69,000,000,000 (which can be written as 69).
- Move the decimal point 10 places to the left: [tex]\( 6.9 \)[/tex].
4. Determine the Power of Ten: After moving the decimal point 10 places to the left to turn 69,000,000,000 into 6.9, your power of ten becomes 10:
[tex]\[
6.9 \times 10^{10}
\][/tex]
5. Conclusion: The number 69,000,000,000 is correctly expressed in scientific notation as [tex]\( 6.9 \times 10^{10} \)[/tex] with the correct number of significant figures. This matches the first option given [tex]\( 6.9 \times 10^{10} \)[/tex].
Therefore, the proper scientific notation for [tex]\( 69,000,000,000 \)[/tex] with significant figures is [tex]\( \boxed{6.9 \times 10^{10}} \)[/tex].
1. Identify the Significant Figures: In the original number [tex]\( 69,000,000,000 \)[/tex], there are two significant figures: '6' and '9'.
2. Form the Scientific Notation: Scientific notation is a way of expressing numbers that are too big or too small in a more compact form, typically using the format:
[tex]\[
a \times 10^n
\][/tex]
where [tex]\( a \)[/tex] is a number such that [tex]\( 1 \leqslant a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer.
3. Convert the Number: Move the decimal point such that there is only one non-zero digit to the left of the decimal point. For the number [tex]\( 69,000,000,000 \)[/tex]:
- Starting from 69,000,000,000 (which can be written as 69).
- Move the decimal point 10 places to the left: [tex]\( 6.9 \)[/tex].
4. Determine the Power of Ten: After moving the decimal point 10 places to the left to turn 69,000,000,000 into 6.9, your power of ten becomes 10:
[tex]\[
6.9 \times 10^{10}
\][/tex]
5. Conclusion: The number 69,000,000,000 is correctly expressed in scientific notation as [tex]\( 6.9 \times 10^{10} \)[/tex] with the correct number of significant figures. This matches the first option given [tex]\( 6.9 \times 10^{10} \)[/tex].
Therefore, the proper scientific notation for [tex]\( 69,000,000,000 \)[/tex] with significant figures is [tex]\( \boxed{6.9 \times 10^{10}} \)[/tex].
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