The Mathematics of The Mathematics of ChemistryChemistry

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

• 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:

1.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.):

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

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

Using Significant Figures Rules

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

00340.003210

Using Significant Figures Rules

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

00340.003210

Using Significant Figures Rules

Rule # 2 – Leading zeros are not significant.

00340.003210

Using Significant Figures Rules

Rule #3 - Zeros to the right of all non-zero digits are only significant if a

decimal point is shown.

00340.003210

How many significant figures?

00340.0

4

Rules #1, 2, and 3

How many significant figures?

800.1

4

Rule #1

How many significant figures?

0800.10

5

Rules # 1, 2, and 3

How many significant figures?

800

1

Rules # 1 and 3

How many significant figures?

800.

3

Rules # 1 and 3

How many significant figures?

0.008

1

Rules # 1 and 2

How many significant figures?

0.180

3

Rules # 1, 2, and 3

Using Significant Figures when Adding and Subtracting in Calculations

1. Determine the number of significant figures in the decimal portion of each of the numbers in the problem.

2. Add or subtract the numbers.

3. Round the answer to match the least number of places in the decimal portion of any number in the problem.

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.

Using Significant Figures when Adding and Subtracting

892.542g

20.629g

0.18g

4.20g

+ 917.551

3

3

2

2

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

A. 0.00263 molesB. .000000190 molesC. 259, 351.6 gramsD. 100,000 milliliters

Scientific Notation

A. 2.63 X 10- 3 moles

B. 1.90 X 10-7 moles

C. 2.593516 X 105 grams

D. 1 X 105 milliliters