## Calculations Using Significant Figures Worksheet

Significant figures are a crucial concept in science and mathematics used to indicate the precision of a measurement. When performing calculations with significant figures, it is important to follow specific rules to ensure the accuracy of the final answer. This worksheet will provide practice problems and examples for calculating with significant figures.

### Introduction to Significant Figures

Significant figures, also known as significant digits, are the numbers in a measurement that convey the precision of the value. They include all the certain digits in a number plus one estimated digit. For example, in the number 3.45, there are three significant figures. The rules for determining significant figures include:

- Non-zero digits are always significant. (1, 2, 3, 4, 5, 6, 7, 8, 9)
- Any zeros between two significant digits are themselves significant. (101, 2003, 40005)
- Leading zeros (zeros that precede all non-zero digits) are not significant. (0.000345, 0.0092)
- Trailing zeros (zeros that follow non-zero digits) in a number containing a decimal point are significant. (4.00, 123.450)

### Rules for Calculations with Significant Figures

When performing calculations with significant figures, there are specific rules to follow to determine the appropriate number of significant figures in the final answer. These rules include:

- For multiplication and division: The final answer should have the same number of significant figures as the measurement with the fewest significant figures.
- For addition and subtraction: The final answer should have the same number of decimal places as the measurement with the fewest decimal places.

### Practice Problems

Now, let’s work through some practice problems to sharpen our skills in performing calculations with significant figures. Make sure to follow the rules outlined above to determine the correct number of significant figures in each answer.

#### Problem 1: Multiplication

Calculate the area of a rectangle with a length of 5.6 cm and a width of 3.2 cm.

Solution:

Area = length x width

Area = 5.6 cm x 3.2 cm = 17.92 cm^{2}

Since the measurement with the fewest significant figures is 3.2 cm with two significant figures, the final answer should also have two significant figures. Therefore, the area of the rectangle is 18 cm^{2}.

#### Problem 2: Division

Calculate the density of a substance with a mass of 25.0 g and a volume of 5.0 cm^{3}.

Solution:

Density = mass / volume

Density = 25.0 g / 5.0 cm^{3} = 5.0 g/cm^{3}

Since the measurement with the fewest significant figures is 5.0 cm^{3} with two significant figures, the final answer should also have two significant figures. Therefore, the density of the substance is 5.0 g/cm^{3}.

#### Problem 3: Addition

Add together 12.14 m, 3.2 m, and 5.678 m.

Solution:

12.14 m + 3.2 m + 5.678 m = 20.018 m

Since the measurement with the fewest decimal places is 3.2 m with one decimal place, the final answer should also have one decimal place. Therefore, the sum of the measurements is 20.0 m.

#### Problem 4: Subtraction

Subtract 102.53 g from 500.242 g.

Solution:

500.242 g – 102.53 g = 397.712 g

Since the measurement with the fewest decimal places is 102.53 g with two decimal places, the final answer should also have two decimal places. Therefore, the difference between the measurements is 397.71 g.

### Conclusion

Calculations using significant figures are essential in science and math to ensure the accuracy and precision of measurements. By following the rules for determining significant figures and applying them to calculations, we can obtain reliable results that reflect the level of precision in our data. Practice is key to mastering the use of significant figures, and the more problems you solve, the more confident you will become in performing calculations with accuracy.