To determine the best approximation for the product of [tex]\( 93,805,674 \)[/tex] and [tex]\( 97 \)[/tex], let's go through the problem step by step.
1. Calculate the product:
- Multiplying [tex]\( 93,805,674 \)[/tex] by [tex]\( 97 \)[/tex] results in [tex]\( 9,099,150,378 \)[/tex].
2. Analyze the product:
- The exact product, [tex]\( 9,099,150,378 \)[/tex], is a large number and can be expressed in scientific notation to make it easier to approximate.
3. Convert to scientific notation:
- In scientific notation, [tex]\( 9,099,150,378 \)[/tex] can be approximated as [tex]\( 9.10 \times 10^9 \)[/tex].
4. Choose the best approximation:
- From the provided options:
- [tex]\( 93,000,000,000 \)[/tex] is [tex]\( 9.3 \times 10^{10} \)[/tex]
- [tex]\( 9,300,000,000 \)[/tex] is [tex]\( 9.3 \times 10^{9} \)[/tex]
- [tex]\( 930,000,000 \)[/tex] is [tex]\( 9.3 \times 10^{8} \)[/tex]
- [tex]\( 93,000,000 \)[/tex] is [tex]\( 9.3 \times 10^{7} \)[/tex]
- [tex]\( 9,300,000 \)[/tex] is [tex]\( 9.3 \times 10^{6} \)[/tex]
- The closest match in scale and magnitude to [tex]\( 9.10 \times 10^9 \)[/tex] is [tex]\( 9.3 \times 10^9 \)[/tex], which corresponds to [tex]\( 9,300,000,000 \)[/tex].
Therefore, the best approximation for [tex]\( 93,805,674 \times 97 \)[/tex] is [tex]\( 9,300,000,000 \)[/tex].
