To solve the problem of multiplying [tex]\(\frac{1}{10}\)[/tex] by 97.43, let's break it down step-by-step:
1. Understand the multiplication problem: We are asked to multiply [tex]\(\frac{1}{10}\)[/tex] by 97.43.
2. Interpret [tex]\(\frac{1}{10}\)[/tex]: The fraction [tex]\(\frac{1}{10}\)[/tex] means dividing by 10. Multiplying a number by [tex]\(\frac{1}{10}\)[/tex] is equivalent to dividing that number by 10.
3. Apply the multiplication rule:
- Multiplying any number by [tex]\(\frac{1}{10}\)[/tex] moves the decimal point one place to the left.
- For example, [tex]\( \frac{1}{10} \times 100 = 10 \)[/tex].
4. Calculate the result:
- We start with the number 97.43.
- Moving the decimal point one place to the left gives us 9.743.
5. Check the possible answers:
- 9,743 is far too large.
- 974.3 is also too large.
- 0.9743 is too small.
After evaluating all options, the correct result is:
9.743
Therefore, the correct answer is: 9.743
