Sure! Let's go through the process of rounding 817.6249 step-by-step for each part of the question.
### Part (a): Rounding to the Nearest 2 Significant Figures
1. Identify Significant Figures: The number 817.6249 has several digits, but we are interested in rounding it to 2 significant figures.
2. Determine the First Significant Figures: The first significant figure is '8', and the second significant figure is '1'.
3. Evaluate the Following Digit: The digit following the second significant figure '1' is '7'.
4. Apply Rounding Rules: Since '7' is greater than 5, we round '1' up to '2'.
5. Reconstruct the Number: After rounding '817.6249', it becomes '820' since after rounding the first two significant figures, the number is represented in a simplified form.
Result for Part (a): [tex]\( \mathbf{820} \)[/tex]
### Part (b): Rounding to the Nearest 2 Decimal Places
1. Identify Decimal Places: The number is 817.6249, and we need to round it to 2 decimal places.
2. Locate the Digits: The digits at the 2nd decimal place are '.62'.
3. Evaluate the Next Digit: The digit following 2 decimal places is '4'.
4. Apply Rounding Rules: Since '4' is less than 5, we keep the second decimal place as it is.
5. Reconstruct the Number: The number after rounding to the nearest 2 decimal places is '817.62'.
Result for Part (b): [tex]\( \mathbf{817.62} \)[/tex]
So, the corrected values are:
- For the nearest 2 significant figures: [tex]\( \mathbf{820} \)[/tex]
- For the nearest 2 decimal places: [tex]\( \mathbf{817.62} \)[/tex]
