To approximate the number [tex]\(9^{1.7}\)[/tex] and round it to three decimal places, follow these steps:
1. Understanding the Expression:
- The expression [tex]\(9^{1.7}\)[/tex] represents 9 raised to the power of 1.7.
2. Calculating [tex]\(9^{1.7}\)[/tex]:
- Using a calculator or computational tool, calculate [tex]\(9^{1.7}\)[/tex].
3. Obtaining the Result:
- The precise result of [tex]\(9^{1.7}\)[/tex] is approximately 41.89983049571471.
4. Rounding to Three Decimal Places:
- To round 41.89983049571471 to three decimal places, look at the fourth decimal place (9 in this case).
- Since the fourth decimal place is 9 (which is greater than or equal to 5), round up the third decimal place from 899 to 900.
5. Final Answer:
- Therefore, [tex]\(9^{1.7} \approx 41.900\)[/tex].
Thus, the approximation of [tex]\(9^{1.7}\)[/tex] rounded to three decimal places is [tex]\(41.900\)[/tex].
