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In division, the result should maintain the same number of significant figures as the number in the calculation with the fewest significant figures. Let's take a closer look at part (a) of the exercise:

We start with the calculation: \( 236.02 \div 108.01 = 2.184376264 \). Both 236.02 and 108.01 have 5 significant figures. Therefore, our result should also have 5 significant figures to be accurate. We then round 2.184376264 to 2.1844.

For another example, in part (c) of the exercise: \( 28.7 \div 7 = 4.1 \). Here, 28.7 has 3 significant figures, while 7 has 1 significant figure. Thus, the answer should also be limited to 1 significant figure, hence rounding 4.1 to 4.

Always remember, use the least number of significant figures from any number in your division operation.

Just like division, multiplication also requires us to apply special rules for significant figures. The product's significant figures should match the number in the problem with the fewest significant figures.

Consider part (b) of the exercise: \( 56.8 \times 300 = 17040 \). Here, 56.8 has 3 significant figures and 300 has only one. The product must be rounded to 1 significant figure, yielding 20000.

This ensures accuracy and consistency in significant figures across all calculations.

Key steps to follow:

• Determine the number of significant figures in each factor.
• Perform the multiplication normally.
• Round the result to the smallest number of significant figures used in the calculation.

Rounding significant figures can sometimes be tricky, but it's crucial for precise calculations. Here are key tips to keep in mind to get it right.

When rounding:

• If the digit after your last significant figure is 5 or greater, round up.
• If it's less than 5, round down.

For instance, in part (a), the calculated value was 2.184376264 and we rounded it to 2.1844 based on 5 significant figures.

In part (b), 17040 was rounded to 20000 to reflect 1 significant figure, due to the limitation imposed by the number 300.

Lastly, in part (c), 4.1 was rounded to 4 since we were confined to 1 significant figure by the number 7.

Points to remember:

• Identify the correct number of significant figures first.
• Apply rounding rules meticulously.

Accurate rounding maintains the integrity and reliability of your calculations.