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# The Mathematics of Chemistry - PowerPoint PPT Presentation

The Mathematics of Chemistry. 4. 5. 2. 8. Significant Figures. 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.

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Presentation Transcript

### The Mathematics of Chemistry

4

5

2

8

Significant Figures

• Measurements always have uncertainty.

• Significant figures are the number of digits that are certain (can be measured) and the first uncertain digit.

• Accuracy refers to how closely a measurement agrees with the accepted or true value.

• Precision refers to reproducibility of measurements.

• Chemistry calculations utilize significantfigures 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.

• Rules for Significant Figures (cont.):

• For values written in scientific notation, the digits in the coefficient are significant.

• In a common logarithm, there are as many digits after the decimal point as there are significant figures in the original number.

Rule #1- Non-zero digits….. are always significant.

00340.003210

Rule #1- …zeros between non-zero digits are always significant.

00340.003210

Rule # 2 – Leading zeros are not significant.

00340.003210

Rule #3 - Zeros to the right of all non-zero digits are only significant if a decimal point is shown.

00340.003210

00340.0

4

Rules #1, 2, and 3

800.1

4

Rule #1

0800.10

5

Rules # 1, 2, and 3

800

1

Rules # 1 and 3

800.

3

Rules # 1 and 3

0.008

1

Rules # 1 and 2

0.180

3

Rules # 1, 2, and 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

the problem.

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.

892.542g

20.629g

0.18g

4.20g

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

• 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.

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

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.

Expanded Notation

Scientific Notation

2.63 X 10- 3 moles

1.90 X 10-7moles

2.593516 X 105 grams

1 X 105 milliliters

A. 0.00263 moles

• .000000190 moles

• 259, 351.6 grams

• 100,000 milliliters