Do Now:

1. How many significant figures are in the following:a) 12.001b) 0.000379c) 0.0003790d) 30100

2. Convert the following to scientific notation:a) 67000b) 67001c) 0.0067d) 0.0067001

Rationale – In general, a calculated answer can NOT be more precise than the least precise measurement it was calculated from.

Calculations with significant figures

Significant Figures in addition and subtraction:

Rule- The answer should be rounded to the same number of decimal places as the measurement with the LEAST number of decimal places.

Example – 7.85 mL +88.1 mL + 0.995 mL

Step 4 – Evaluate if the answer makes sense – Double check the number of your answer has the same decimal place as the least number of decimal places of any of the numbers used in the addition and/or subtraction problem

Method 1

Step 1 – Circle the measurement with the least number of decimal places. (88.1 mL)

Step 2 – Add up all of the values: 7.85 mL + 88.1 mL + 0.995 mL = 96.945 mL

Step 3 – Round the answer to the decimal place in the circles number: 96.9 mL

Example – 7.85 mL +88.1 mL + 0.995 mL

Method 2

Step 1 – Setup the numbers above each other with the decimal places aligned:

7.85 mL 88.1 mL+ 0.995 mL

Step 2 – Perform the math

7.85 mL 88.1 mL+ 0.995 mL 96.945 mL

Step 3 – Look at the math problem and round the answer to rightmost decimal place that has a number in EVERY column (you can circle the column if that helps visualize it).

Round to 96.9 mL (final answer)

Step 4 – Evaluate if the answer makes sense – Double check the number of your answer has the same decimal place as the least number of decimal places of any of the numbers used in the addition and/or subtraction problem

1. 6.12 g + 1.7 g + 19.1 g

2. 22 g – 3.6 g

3. 12.01 g +1.0079 g + 12.01 g +1.0079 g

Practice Problems

Rule – In calculations involving multiplication and division, you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures.

Significant Figures in Multiplication and Division

Example – 11.5 x 2.9

Step 1 – Circle the number with the fewest number of significant figures used in the multiplication and/or division. (2.9)

Step 2 – Write the number of significant figures next to the circled number.(2.9) 2 sig figs

Step 3 – Perform the math operation(s) 11.5 x 2.9 = 33.35

Step 4 – Round answer to the correct number of significant figures. 33

Step 5 – Evaluate the answer. Double check your final answer with the numbers used in the problem. Does the final answer have the same number of significant figures as the fewest number of significant figures used in any of the numbers in the calculation (compare again with your circled number from Step 1).

Practice Problems

1. 15 ÷ 3

2. 15 ÷ 3.0

3. 112 x 33.55 x 1.7

4. 6.75 x 110.2 ÷ 0.33

5. 11 x 9

= 5

= 5.0

= 6400

= 2300

= 100

Conversion Factors

A Conversion Factor is a ratio of equivalent measurements.

Creating a conversion factor

Step 1 – Setup an equation of two equal measurements.

1 dollar = 4 quarters

Step 2 – Divide both sides of the equation by the right hand side

1 dollar = 4 quarters4 quarters = 4 quarters

Step 3 – Simplify the equation

1 dollar = 1 4 quarters

Step 4 – Flip the equation if needed (the same thing as having divided both sides of the equation by the left hand side instead of the right hand side).

4 quarters = 1 1 dollar

Setup a conversion factor for the following:

1. Seconds in a minute

2. Milliliters in a liter

3. Kilograms in a gram

Practice Problems