1. Measurement & Calculation
Chapter 2
Measurement & Calculation

3. Units of Measurement Why is it important that measurements have units?
Is 2 inches the same amount of length as 2 centimeters?
A student measures the mass (or weight – not exactly the same thing but we will discuss that later) of a block of copper metal. He reports in his lab notebook that the sample weighs Is this an acceptable record of data?
A quantity has _______, ______ or ________.
magnitude, size or amount
SI stands for Le Systeme International d’Unites. We usually just say “international standard”.
NIST stands for National Institute of Standards and Technology. This organization plays the main role in maintaining standards.

4. Units of Measurement
Make sure you know these for tests.

5. Units of Measurement
Mass is a measure of the quantity of matter. What is the SI unit for mass?
What is the difference between mass and weight?
How is mass measured?
How is weight measured?
What is the SI unit for length?
Derived units are combinations of SI base units.
EXAMPLES: square meter, m2 (length X width). What is this dimension? Grams per milliliter, g/mL (mass/volume). What is this dimension?
What term describes the amount of space occupied by an object?

6. Units of Measurement
Density is the ratio between mass to volume and is a measure of how massive an object is compared with its size.
What is the density of a block of marble that occupies 310. cm3 and has a mass of 853g?
What is the volume of a sample of liquid mercury that has a mass of 76.2g given that the density of mercury is 13.6g/mL?
Diamond has a density of 3.26 g/cm3. What is the mass of a diamond that has a volume of cm3?
How many inches are in a foot?
1 ft = 12 inches  1ft/12in OR 12in/1ft  from these equalities, we can convert from one unit to another (IE, how many inches are in 3.45ft?). We call these equalities ____________.
Dimensional analysis is a math operation that can convert from one unit to another. This is VERY important and will be seen throughout the stent of this course. Please practice this technique and if you have questions, ASK!

7. Units of Measurement
Express a mass of 5.712g in milligrams (mg) and in kilograms (kg). Don’t forget your conversion factors!
Express a length of 16.45m in centimeters (cm) and in kilometers (km).
Express a mass of 0.014mg in grams (g).

8. Using Scientific Measurements
Accuracy is the closeness of a measurement to an accepted or correct value.
Precision is the closeness of a SET of measurements of the same quantity made in the same way.
A chemistry student measures the density of a sample of saturated salt water. She finds the density, after measuring both mass and volume, to be 1.025g/mL. To check the accuracy of her measurement, she consults the literature for an accepted density value for saturated salt water. She finds the theoretical density to be g/mL. Was she checking the accuracy or the precision of her measurement? Depending on your choice, was she either accurate or precise?

9. Using Scientific Measurements

10. Using Scientific Measurements
Percentage error quantitatively compares the accuracy of an individual value to the correct/accepted value. It is a calculation.
A chem student calculates the density of a known substance as g/mL. The theoretical/accepted/expected density of this substance is 2.99 g/mL. Calculate the % error of the student’s measurement & calculation.

11. Using Scientific Measurements
Significant figures are numbers in a measurement representing a quantity that consists of all known digits. IE, some scales measure to only 1 decimal place while others measure out to four or more decimal places.
When recording measurements as data, we must report only digits that are certain. If one measurement was made with a scale to only one decimal place while the other was measured to four, we must only record digits that are certain.
The significance of zeros in a number depends on their location.
You must memorize the rules for determining significant zeros in measurement. You will find these rules on page 47 table 5.

12. Using Scientific Measurements

14. Using Scientific Measurements
Often, answers given on a calculator have more digits than are justified by the measurements so we need to round.
EXAMPLE: What is the density of a substance with a mass of 154g and a volume of 327mL? Enter into calculator 154/327 = g/mL. This answer contains digits not justified by the measurements used to calculate it. Why?
Because both parameters (mass and volume) are only reported to 3 sig figs. Therefore, the answer must be reported to only 3 sig figs.
So what would be the appropriate reported density?
0.471g/mL

15. Using Scientific Measurements
When using conversion factors, we do not consider significant figure rules.
Scientific notation (sci. not.) is when numbers are written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number.
RULES FOR SCI. NOT. :
Determine M by moving the decimal point in the original number to the left or right so that only one nonzero digit remains to the left of the decimal.
Determine n by counting the number of places that you moved the decimal point. If you moved it to the left, n = positive. If you moved it to the right, n = negative.

17. Using Scientific Measurements
Direct proportionality: as one parameter goes up, the other goes up. Two quantities are directly proportional to each other if dividing one by the other gives a constant value. Example, as the mass of a sample goes up, the volume of the sample goes up. Therefore, mass and volume are directly proportional.
Inverse proportionality: as one parameter goes up, the other goes down. Two quantities are inversely proportional to each other if their product is constant. Example, the speed of travel and the time required to cover a fixed distance  the greater the speed, the less amount of time needed to cover the same distance.

18. Using Scientific Measurements