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When performing addition, it's crucial to keep track of decimal places, as they determine how precise your answer can be. Each number in an addition operation may have a different number of decimal places. The result of the addition should match the smallest number of decimal places among the numbers being added.

For example, when we add 14.3505 and 2.65, 2.65 has two decimal places while 14.3505 has four. We must, therefore, round our final answer to two decimal places to align with 2.65. This ensures that the level of precision of the numbers is respected in your answer.

By applying this rule, we get:

• Initial sum: 16.0005
• Rounded result: 16.00

This rule helps prevent mistakes that could arise from assuming more precision than the numbers inherently have.

Much like addition, subtraction requires attention to decimal places to retain the correct level of precision in the answer. Again, you must find the number in the problem that has the least number of decimal places. Your subtraction result should be rounded to this level.

In the example of subtracting 140.7389 from 952.7, the number 952.7 guides the formatting of the final result since it only has one decimal place. After carrying out the subtraction, we ensure the final answer has just one decimal place.

Let's see how it looks in practice:

• Initial difference: 811.9611
• Rounded result: 812.0

This practice avoids overestimating how precisely you know the answer.

When multiplying numbers, the rule of significant figures takes the lead over decimal places. The result of a multiplication should contain the same number of significant figures as the number with the least significant figures in the operation.

Take the multiplication of (3.29 脳 10鈦�) by 0.2501. The number 3.29 has the fewest significant figures, that is, three. Therefore, our result must also be expressed in three significant figures.

In this case, the calculation gives:

• Initial product: 82229.0
• Rounded result: 8.22 脳 10鈦�

Following significant figure rules ensures the accuracy of your result reflects the precision of your measurements or calculations.

In division, as with multiplication, significant figures dictate how you should present your final answer. Your result should match the number with the fewest significant figures in the original problem.

For instance, divide 0.0588 by 0.677. Here, 0.0588, having three significant figures, determines the precision of our answer. Therefore, the quotient should also be reported with three significant figures.

Here's how it unfolds:

• Initial quotient: 0.086838399
• Rounded result: 0.0869

This approach respects the inherent uncertainty in your calculations, delivering a result that remains consistent with the precision of the input values.