The Mathematics of Chemistry 4 5 2 Significant Figures 8

Uncertainty in Measurement Measurements always have uncertainty. Significant figures are the number of digits that are certain (can be measured) and the first uncertain digit.

Accuracy and Precision Accuracy refers to how closely a measurement agrees with the accepted or true value. Precision refers to reproducibility of measurements. Chemistry calculations utilize significant figures to communicate uncertainty.

Rules for Significant Figures: Non-zero digits and zeros between non-zero digits are always significant. 2. Leading zeros are not significant. 3. Zeros to the right of all non-zero digits are only significant if a decimal point is shown. At this time, it is important to emphasize the use of the STAAR Chemistry Reference Materials. Point out to the students where this information is found, and encourage them to reference it with this unit of study of the STAAR.

Rules for Significant Figures: For values written in scientific notation, the digits are only significant if a decimal point is shown. In a common logarithm, there are as many digits after the decimal point as there are significant figures in the original number. Rule 5 will not be included in this unit.

Rules for Finding Significant Figures Rule #1- Non-zero digits and zeros between non-zero digits are always significant. 00340.003210 As you go through this guided practice to determine significant figures, continually refer the students to the rules on the STAAR Chemistry Reference Materials and have them identify the supporting rule. Based on Rule 1 alone, there a five significant figures so far.

Rules for Finding Significant Figures Rule #1- Non-zero digits and zeros between non-zero digits are always significant. 00340.003210 Point out the three 0’s that are significant due to this rule. These, coupled with the other numbers that were described as non-zero digits, total eight significant figures.

Rules for Finding Significant Figures Rule #2 - Zeros to the right of all non-zero digits are only significant if a decimal point is shown. 00340.003210 This final 0 contributes as a significant digit too, making the total number of significant figures to total nine.

Rules for Finding Significant Figures These zeros are not significant. There is not a rule that supports counting them. 00340.003210

How many significant figures? 00340.0 4 Rule #3 You are encouraged to make these slides interactive with the students. Ask them to make the determination and identify the rule(s) from the STAAR reference chart. Then, have them turn to a partner and discuss the answer. Next, call on a group to share their consensus and the supporting rule. This allows you to guide the practice, but keeps the students engaged in the work and allows you to check for understanding and misconceptions along the way.

How many significant figures? 800.1 4 Rule #1

How many significant figures? 0800.10 5 Rules # 1 and 3

How many significant figures? 800 1 Rule #3

How many significant figures? 800. 3 Rule #3

How many significant figures? 0.008 1 Rule #2

How many significant figures? 0.180 3 Rule # 3

Using Significant Figures when Adding and Subtracting in Calculations Determine the number of significant figures in the decimal portion of each of the numbers in the problem. 2. Add or subtract the numbers. Round the answer to match the least number of places in the decimal portion of any number in For purposes of calculations, do not use constants or coefficients to determine the number of significant figures.

Using Significant Figures when Adding and Subtracting Give it a try! Add 0.03 g of NaCl to 155 g of water. What is the total mass? Answer: 155 g because the mass of water has no decimal places, so the final answer must be written with no decimal places. When referring to the least precise number, that can also be referenced as the number with the least number of decimal places. For the example, .03 g is represented using two decimal places and the 155 g has 0 decimal places; therefore, the answer should be recorded with 0 decimal places after the calculation is made.

Using Significant Figures when Adding and Subtracting 3 3 2 + 2 917.551 The least amount of significant figures to the right of the decimal in the numbers is 2; therefore, the answer should only have 2 significant figures to the right of the decimal. 917.55 g

Using Significant Figures when Multiplying and Dividing Determine how many significant figures each numbers being multiplied or divided has, and note which number has the fewest. Complete the calculation. Write the answer using the same number of significant figures as the least number of significant figures found in the numbers used in the calculation.

Using Significant Figures when Multiplying and Dividing 28.3 cm X 5.0 cm = ____cm2 28.3 has 3 significant figures, and 5.0 has 2 significant figures; therefore, the answer 141.5 should be written 140, so that it only has 2 significant figures. 140 cm2

Try it! 454.02 g of aluminum hydroxide multiplied by 5.2 g equals how many grams? 454.02 g X 5.2 g = _____ g Rule: Write the answer using the same number of significant figures as the least number of significant figures found in the numbers used in the calculation.

Scientific Notation Expanded Notation Scientific Notation 2.63 X 10- 3 moles 1.90 X 10-7 moles 2.593516 X 105 grams 1 X 105 milliliters A. 0.00263 moles .000000190 moles 259, 351.6 grams 100,000 milliliters Engage the students in this practice of writing in both expanded and scientific notation. Be sure to point out that determining the number of significant digits is the first step as this number is conserved in both representations of the number. Continue to emphasize that the rules for determining significant figures (on STAAR reference materials) will be embedded within the content and calculations and not in isolation. Put the rules into practice.