1. Chapter 3: Scientific measurement

2. 3.1 Measurement and their uncertainty

3. Using and expressing measurements
Measurement: a quantitiy that has both a number and a unit.
60 mph, 85 degrees Farienheit
Measurements are fundamental to the experimental sciences. Because of that, it is important to be able to make measurements and decide whether a measurement is correct.
Units typically used in science are those of the International System of Measurements (SI).

4. In science, measurements can be VERY large or VERY small== A LOT of zeros.
To avoid writing , we can use scientific, or exponential, notation.
In scientific notation, a given number is written as the product of two numbers: a coefficient and 10 raised to a power.
can be written 4.5 x 10-14

5. Accuracy and precision
Accuracy: measure of how close a measurement comes to the actual or true value of whatever is measured
Precision: measure of how close a series of measurements are to one another
To evaluate accuracy, the measured value must be compared to the correct value. To evaluate precision, you must compare values from two or more repeated measurements
Look at darts on a dart board.

6. High Accuracy
High Precision
Low Accuracy
High Precision
Low Accuracy
Low Precision

7. Determining error Error=experimented value - accepted value
Experimental value: value measured in lab
Actual value: correct value based on reliable resources
Always in this order, value can be positive or negative

8. Percent error, also known as relative error, is calculated by dividing the absolute error (remember absolute value is always positive) by the accepted value and multiplying by 100.
Just because a measuring device works, does not mean it is always accurate.
Scale example– Complete Checkpoint in Figure 3.3:
An individual steps on a scale which has not properly been zeroed, so the reading for that person’s weight is inaccurate. There is a difference between the person’s actual weight and the measured value. What is the percent error of a measured value of 114 lbs. if the person’s actual weight is 107 lbs.?

9. Significant figures in measurements
Significant figures: include all the digits that are known, PLUS a last digit that is estimated
Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation.
Instruments differ in the number of significant figures that can be obtained from their use.

10. Rules for determining whether a digit in a measured value is significant (pg 66-67)
Look at hand out
Conceptual Problem 3.1 pg 68

11. Significant figures in calculations
In general, a calculated answer cannot be more precise than the least precise measurement from which was calculated
Type 7.7 x 5.4 in your calculator, what do you get?
41.48? According to our general rule, is this answer correct?
No, we have to round to 2 significant figures: 42

12. How do we round??
First, we must decide how many significant figures the answer should have.
Look at the given measurements
Look at the last number
Is it more than 5? Round up
Less than 5? Drop it
Let’s try some!! Write these down!! Page 69

13. 314.721 meters- Round to four significant figures
meters- Round to two significant figures
8792 meters- Round to two significant figures

14. Addition and subtraction
With addition and subtraction, the answer should be rounded to the same number of decimal places (NOT digits) as the measurement with the least number of decimal places.
Sample Problems! Write them down!

15. 12.52 meters + 349.0 meters + 8.24 meters

16. Multiplication and division
You must round the answer to the same number of significant figures as the measurement with the least number of significant figures.
Sample problems!

17. 7.55 meters x 0.34 meters
meters / 8.4

18. 3.2 the international system of units (si)

19. Measuring with si units
Why do we need units attached to a numerical value?
Without, it is impossible to communicate measurement. “Walk 5 in that direction.” What?!
The standards used in science are the metric system, which is based on multiples of 10.
The International System of Units is a revised version of the metric system, which includes 7 base units.
From these 7 base units, all measurements can be derived

20. Si base units Quantity SI base unit Symbol Length *Meter m Mass
*Kilogram kg
Temperature
*Kelvin K
Time
*Second s
Amount of substance
*Mole
mol
Luminous intensity
Candela cd
Electric current
ampere A
* Units commonly used by chemist

21. Different quantities require different units
Units and quantities
Different quantities require different units
You wouldn’t measure length in kilograms
Let’s look at the different units!

22. Units of length Basic unit of length is meter.
For very large or very small lengths, a unit of length that has a prefix can be used.
Large: kilometers, 1 km=1000 m
Small: millimeter, 1000 mm= 1 m
Common metric units of length include centimeter, meter, and kilometer.

23. Units of volume
Volume: space occupied by any sample of matter. V=length x width x height
Those values are derived from units of length, answer is in cubic measurements
Meter x meter x meter= cubic meter
A more convenient unit of volume is the liter (L).
A Liter is a non-SI unit
Common metric units of volume include the liter, milliliter, cubic centimeter, and microliter.
The volume of any sold, liquid, or gas will change with temperature
Therefore, accurate-measuring devices are calibrated at a given temp- usually 20 degrees Celsius, about normal room temperature.

24. Units of mass Weight vs Mass
Weight: force that measures the pull on a given mass by gravity
Mass: measure of the quantity of matter
Weight of an object can change, depending on location. Mass remains the same
Mass is measured in kilograms
Common metric units of mass include the kilogram, gram, milligram, and microgram

25. Units of temperature
Temperature: a measure of how hot or cold an object is.
Temperature determines the direction of heat transfer.
Heat moves from higher temperatures to lower temperatures.
Holding Ice vs holding cup of coffee
With most substances, they expand with an increase in temperature. (EXCEPT water).
Scientists use two equivalent units of temperature, the degree Celsius and the kelvin.
Celsius sets freezing at 0C and boiling at 100C
Kelvin scale sets freezing at K and boiling at K
K = C + 273
C = K - 273
Sample problems pg 78

26. Sample Problem
Pg 78
Liquid nitrogen boils at 77.2 K. What is this temperature in degrees Celsius?
The element silver melts at 960.8C and boils at 2212C. Express these temperatures in kelvins.

27. Units of energy Energy: the capacity to do work or to produce heat
The joule and the calorie are common units of energy
Joule (J): SI unit of energy
Calorie (cal): quantity of heat that raises the temperature of 1 g pf pure water by 1C
Equation:
1 J = cal cal = J

28. 3.3 conversion problems

29. Conversion factors
Numbers in everyday situations can be expressed differently.
You can have 1 dollar or 4 quarters or 10 dimes and so on
Same can be true of scientific quantities
1 meter = 10 decimeters = 100 centimeters = 1000 millimeters
Conversion factor is the ratio of equivalent measurements
Example: 100cm/1m or 1m/100 cm
Note: when a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same.

31. Dimensional analysis
Dimensional analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements.
Sample problems pg 82
Remember, there may be more than one way to solve a problem. Dimensional analysis provides an alternate approach to problem solving.
More problems on page 83

32. Converting between units
Problems in which a measurement with one unit is converted to an equivalent measurement with another unit are easily solved using dimensional analysis.
Sample Problem pg 84
In some cases more than 1 conversion factor is needed. Remember breaking down problems make them easier to solve!!
Sample problems pg 85
Sometimes you have to convert a ration that uses two units: converting miles per hour to kilometers per second
Sample problems pg 86

33. 3.4 Density

34. Determining density Which weighs more?
Density is the ratio of mass of an object to its volume.
Density= 𝑚𝑎𝑠𝑠 𝑣𝑜𝑙𝑢𝑚𝑒
Density is an intensive property that depends only on the composition of a substance, not on the size of the sample.
Helium is less dense than air, so a balloon filled with helium floats.

35. Density and temperature
Remember that the volume of most substances increase as temperature increases. Mass stays the same with temperature and volume changes.
If volume changes with temperature changes, but mass does not, density must change with temperature change as well.
Density of a substance generally decreases as temperature increases. (Again water is an exception)
Sample problem pg 91 and 92