Operations with Significant Figures: Videos & Practice Problems

Understanding significant figures is crucial in mathematical operations involving addition, subtraction, multiplication, and division. For addition and subtraction, round to the least number of decimal places. In multiplication and division, round to the least number of significant figures. When combining operations, follow the order of operations and round to the most significant figures. This ensures precision in calculations, which is essential in scientific contexts, such as determining values in physics and chemistry.

Operations with Significant Figures

Understanding significant figures is crucial when performing mathematical operations, as it ensures that the precision of your measurements is accurately reflected in your results. There are specific rules to follow for addition, subtraction, multiplication, and division to determine the appropriate number of significant figures in your final answer.

When adding or subtracting numbers, the result should be rounded to the same number of decimal places as the measurement with the least decimal places. For example, if you add 12.34 (two decimal places) and 5.6789 (four decimal places), the sum is 18.0189, which rounds to 18.02, maintaining two decimal places.

In cases where you are multiplying or dividing, the final answer should reflect the number of significant figures of the measurement with the least significant figures. For instance, if you multiply 2.5 (two significant figures) by 3.678 (four significant figures), the product is 9.195, which rounds to 9.2, as it should only have two significant figures.

When operations involve both addition/subtraction and multiplication/division, follow the order of operations. First, perform the multiplication or division, then add or subtract. The final result should be rounded to the highest number of significant figures from any of the measurements involved. For example, if you calculate (2.5 × 3.678) + 4.68, you first find the product (9.195) and then add 4.68, resulting in 13.875. If the product has three significant figures and the addition has two, round the final answer to three significant figures, yielding 13.9.

By applying these rules consistently, you can ensure that your calculations maintain the appropriate level of precision, which is essential in scientific and mathematical contexts.

What is the area of a sidewalk that is 2.293 m wide and 90 m long? Write your answer with the correct number of significant figures.

• A. 206.4 m²
• B. 210 m²
• C. 206.37 m²
• D. 200 m²

Answer: (D)

Volume of Two Blocks

In this problem, we are tasked with finding the total combined volume of two blocks, Block A and Block B. The dimensions of Block A are given as 0.50 meters, 0.875 meters, and 2.250 meters, while the volume of Block B is provided as 2.6 cubic meters. To determine the total volume, we will calculate the volume of Block A and then add it to the volume of Block B.

The volume of a rectangular block (or cube) is calculated using the formula:

Volume (V) = Length × Width × Height

For Block A, we substitute the given dimensions into the formula:

V_A = 0.50 m × 0.875 m × 2.250 m

Calculating this gives:

V_A = 0.984375 m³

Next, we need to consider significant figures. The dimensions of Block A have 2, 3, and 4 significant figures respectively. The limiting factor here is the measurement with 2 significant figures (0.50 m). Therefore, we will keep track of significant figures without rounding at this stage.

Now, we add the volume of Block A to the volume of Block B:

V_Total = V_A + V_B = 0.984375 m³ + 2.6 m³

When performing addition, we focus on the decimal places. The number 2.6 has one decimal place, while 0.984375 has three. Thus, we will round our final answer to one decimal place:

V_Total = 3.584375 m³

Rounding this to one decimal place gives us:

V_Total = 3.6 m³

In summary, the total combined volume of Block A and Block B is 3.6 cubic meters. It is crucial to maintain accuracy by avoiding premature rounding during intermediate calculations and only rounding the final result according to the rules of significant figures.

Here’s what students ask on this topic:

What are the rules for significant figures in addition and subtraction?

When performing addition or subtraction, the result should be rounded to the same number of decimal places as the number with the least number of decimal places in the original numbers. For example, if you add 12.34 (2 decimal places) and 1.2 (1 decimal place), the result should be rounded to 1 decimal place. This ensures that the precision of the result is consistent with the least precise measurement.

How do you determine significant figures in multiplication and division?

In multiplication and division, the result should be rounded to the same number of significant figures as the number with the least number of significant figures in the original numbers. For instance, if you multiply 4.56 (3 significant figures) by 1.2 (2 significant figures), the result should be rounded to 2 significant figures. This rule ensures that the precision of the result matches the least precise measurement.

What is the rule for significant figures when combining addition/subtraction with multiplication/division?

When combining addition/subtraction with multiplication/division, follow the order of operations (PEMDAS/BODMAS). Perform the multiplication or division first, then the addition or subtraction. Round the intermediate result to the appropriate number of significant figures before proceeding. Finally, round the final result to the most significant figures among the numbers involved. This approach maintains the precision of the calculations throughout the process.

How do you round numbers to the correct number of significant figures?

To round a number to the correct number of significant figures, identify the digit at the desired place. If the digit immediately to the right is 5 or greater, round up the identified digit. If it is less than 5, leave the identified digit unchanged. For example, to round 3.456 to 2 significant figures, look at the third digit (6). Since it is greater than 5, round up the second digit (4) to 5, resulting in 3.5.

Why are significant figures important in scientific calculations?

Significant figures are crucial in scientific calculations because they convey the precision of measurements and ensure that results are not over-interpreted. They help maintain consistency and accuracy in reporting data, which is essential in fields like physics and chemistry. By using significant figures, scientists can communicate the reliability of their measurements and calculations, avoiding misleading conclusions based on overly precise or imprecise data.