1. Numbers are central to Science
You can not “do” Chemistry without basic numerical skills.
Measurement and error:
Every measurement except for counting the measured value contains some type of inherent error.

2. Error Types
Random Error: Error that occurs randomly and that normally cannot be avoided.
There is an equal probability of a + and a - deviation from the measured value.
Systematic or Determinate Error: A type of error with both a definite magnitude and sign.
Typical sources are Instrumental errors and Method errors.

3. Figure: UN
Title:
Accuracy, precision, and significant figures
Caption:
The balance on the left has a low or poor precision than the balance on the right (which has high or good precision). The number of reported significant figures often indicates this - it would be senseless to report to a number of decimals that cannot be trusted due to low precision.
Notes:

4. Accuracy: • Indicates how close a measured value is to the true value
Accuracy: • Indicates how close a measured value is to the true value. • Effected by both random and systematic error. • Determined from a comparison of average measured values with known values. Precision: • A measure of the reproducibility of the method. • How close are the results obtained in the same way? • Determined from a comparison of measured values with the average measured value. • Standard deviation is an effective monitor of random error.

6. Significant Figures
There are two types of numbers;
Counting numbers: Counting Numbers are exact, i.e. 30 students in Chem. 121.
Measured numbers: Measured numbers have units and significant figures.
Significant figures reflect the magnitude of certainty or the precision of the measurement.

7. Figure: 01-12
Title:
Determining the number of significant figures in a quantity
Caption:
The quantity shown here, , has seven significant figures. All nonzero digits are significant, as are the indicated zeros. Scientific notation allows one to see just the significant figures ( x 10-3).
Notes:

8. For a measurement, the number should include all digits known with certainty and the first uncertain digit.
For single measurements, the first digit for which you are uncertain is generally the one resulting from estimating to 1/10th of the smallest scale division.

9. For example…
If one is measuring the diameter of a coin using a ruler with the smallest divisions being in increments of 1 mm, the measurement is made to the nearest 1/10th of a millimeter or 0.1 mm.

10. If an object is said to be 23
If an object is said to be 23.5 mm long, then the certainty of the measurement is also evident. i.e., between 23.4 and inches.
The final digit, “5" is estimated and has some uncertainty associated with it.
The value 24.5 has 3 significant digits.
Writing the measurement as 2 cm (1 sig. fig.) or 24 mm (2 sig. figs.), or (4 sig. fig.) mm is not correct in that it does not convey the precision of the measurement.

11. How many significant figures are in;
(a) 23 inches (b) mm
(c) Liters (d) 6 people
(e) miles (f) 100 Km

12. Significant Figures (Functions)
Addition & Subtraction :
same digits after decimal as least
Multiplication & Division:
same number of sig. figs. as least
• 2.8 x = → round to 13
• (6.85) ÷(112.04) = →round to (6.11 x 10-2)

15. Physical quantities
SI Units used in Chemistry and most sciences are based on a French System.

16. How accurate is the measurement?
Absolute Error = experimental value – accepted value
Note that the answer is expressed to the proper number of significant figures, it has units, and its value can be + or -

17. In SI System large and small numbers related through descriptive prefixes

19. Figure: 01-11
Title:
Measuring the volume of an irregularly shaped solid
Caption:
When submerged in a liquid, an irregularly shaped solid displaces a volume of liquid equal to its own. The necessary data can be obtained by two mass measurements of the type illustrated here; the required calculations are like those in Example 1-3. Mass ratioed against volume is density.
Notes:

21. Temperature: There are 3 temperature scales currently in use
Temperature: There are 3 temperature scales currently in use. • Fahrenheit scale: Common in US • Kelvin scale: SI base temperature Scale. AKA absolute temperature scale. • Celsius scale: units identical magnitude to Kelvin

22. Problem Solving (Dimensional Analysis):
All measured numbers must have units to carry any meaning. The careful consideration of these units (the dimensions) can provide insight into problem solving.
For example;
You know you live 3.0 miles away from a mall. Can you determine how many feet you are from the mall, given there are 5280 feet in a mile?
3.0 mile x 5280 feet/mile = feet = 1.6 x 104 feet

23. Problem Solving Recipe:
1. Write down the given number(s) with its units.
2. Write a ratio with the given number in the denominator (at the bottom) and the unit sought in the numerator (on top).
3. Insert numbers into the ratio such that numerator and denominator are equal.
4. Multiply Steps 1 and 3 together.

26. Physical quantities
SI Units used in Chemistry and most sciences are based on a French System.

27. How accurate is the measurement?
Absolute Error = experimental value – accepted value
Note that the answer is expressed to the proper number of significant figures, it has units, and its value can be + or -

28. In SI System large and small numbers related through descriptive prefixes

30. Figure: 01-11
Title:
Measuring the volume of an irregularly shaped solid
Caption:
When submerged in a liquid, an irregularly shaped solid displaces a volume of liquid equal to its own. The necessary data can be obtained by two mass measurements of the type illustrated here; the required calculations are like those in Example 1-3. Mass ratioed against volume is density.
Notes:

32. Temperature: There are 3 temperature scales currently in use
Temperature: There are 3 temperature scales currently in use. • Fahrenheit scale: Common in US • Kelvin scale: SI base temperature Scale. AKA absolute temperature scale. • Celsius scale: units identical magnitude to Kelvin

33. Problem Solving (Dimensional Analysis):
All measured numbers must have units to carry any meaning. The careful consideration of these units (the dimensions) can provide insight into problem solving.
For example;
You know you live 3.0 miles away from a mall. Can you determine how many feet you are from the mall, given there are 5280 feet in a mile?
3.0 mile x 5280 feet/mile = feet = 1.6 x 104 feet

34. Problem Solving Recipe:
1. Write down the given number(s) with its units.
2. Write a ratio with the given number in the denominator (at the bottom) and the unit sought in the numerator (on top).
3. Insert numbers into the ratio such that numerator and denominator are equal.
4. Multiply Steps 1 and 3 together.